LMFDB - Embedded newform 96.2.n.a.37.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [96,2,Mod(13,96)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(96, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("96.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 96 = 2^{5} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	96.n (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.766563859404$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			37.5
Character	$\chi$	$=$	96.37
Dual form			96.2.n.a.13.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.605567 - 1.27800i) q^{2} +(-0.382683 - 0.923880i) q^{3} +(-1.26658 - 1.54783i) q^{4} +(1.60930 + 0.666593i) q^{5} +(-1.41246 - 0.0704008i) q^{6} +(-0.589445 - 0.589445i) q^{7} +(-2.74513 + 0.681373i) q^{8} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(0.605567 - 1.27800i) q^{2} +(-0.382683 - 0.923880i) q^{3} +(-1.26658 - 1.54783i) q^{4} +(1.60930 + 0.666593i) q^{5} +(-1.41246 - 0.0704008i) q^{6} +(-0.589445 - 0.589445i) q^{7} +(-2.74513 + 0.681373i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(1.82644 - 1.65302i) q^{10} +(-0.657053 + 1.58627i) q^{11} +(-0.945311 + 1.76249i) q^{12} +(3.87213 - 1.60389i) q^{13} +(-1.11026 + 0.396364i) q^{14} -1.74189i q^{15} +(-0.791564 + 3.92090i) q^{16} +7.96502i q^{17} +(0.475483 + 1.33188i) q^{18} +(3.97306 - 1.64569i) q^{19} +(-1.00653 - 3.33521i) q^{20} +(-0.319006 + 0.770147i) q^{21} +(1.62936 + 1.80031i) q^{22} +(-0.452012 + 0.452012i) q^{23} +(1.68002 + 2.27542i) q^{24} +(-1.39004 - 1.39004i) q^{25} +(0.295061 - 5.91986i) q^{26} +(0.923880 + 0.382683i) q^{27} +(-0.165784 + 1.65894i) q^{28} +(-1.69130 - 4.08316i) q^{29} +(-2.22614 - 1.05483i) q^{30} -9.32808 q^{31} +(4.53157 + 3.38598i) q^{32} +1.71696 q^{33} +(10.1793 + 4.82335i) q^{34} +(-0.555673 - 1.34151i) q^{35} +(1.99009 + 0.198877i) q^{36} +(0.810329 + 0.335649i) q^{37} +(0.302752 - 6.07415i) q^{38} +(-2.96360 - 2.96360i) q^{39} +(-4.87193 - 0.733351i) q^{40} +(-6.65023 + 6.65023i) q^{41} +(0.791071 + 0.874066i) q^{42} +(-2.22413 + 5.36952i) q^{43} +(3.28748 - 0.992122i) q^{44} +(-1.60930 + 0.666593i) q^{45} +(0.303949 + 0.851396i) q^{46} -8.50500i q^{47} +(3.92535 - 0.769153i) q^{48} -6.30511i q^{49} +(-2.61824 + 0.934713i) q^{50} +(7.35872 - 3.04808i) q^{51} +(-7.38691 - 3.96196i) q^{52} +(1.10759 - 2.67397i) q^{53} +(1.04854 - 0.948979i) q^{54} +(-2.11479 + 2.11479i) q^{55} +(2.01974 + 1.21647i) q^{56} +(-3.04084 - 3.04084i) q^{57} +(-6.24248 - 0.311142i) q^{58} +(-1.92200 - 0.796118i) q^{59} +(-2.69615 + 2.20624i) q^{60} +(-4.70435 - 11.3573i) q^{61} +(-5.64878 + 11.9213i) q^{62} +0.833602 q^{63} +(7.07146 - 3.74091i) q^{64} +7.30055 q^{65} +(1.03974 - 2.19428i) q^{66} +(4.54765 + 10.9790i) q^{67} +(12.3285 - 10.0883i) q^{68} +(0.590582 + 0.244627i) q^{69} +(-2.05095 - 0.102225i) q^{70} +(9.09946 + 9.09946i) q^{71} +(1.45930 - 2.42290i) q^{72} +(1.65052 - 1.65052i) q^{73} +(0.919668 - 0.832343i) q^{74} +(-0.752286 + 1.81618i) q^{75} +(-7.57944 - 4.06522i) q^{76} +(1.32231 - 0.547721i) q^{77} +(-5.58215 + 1.99283i) q^{78} -0.580469i q^{79} +(-3.88750 + 5.78224i) q^{80} -1.00000i q^{81} +(4.47185 + 12.5262i) q^{82} +(3.33576 - 1.38172i) q^{83} +(1.59610 - 0.481685i) q^{84} +(-5.30942 + 12.8181i) q^{85} +(5.51540 + 6.09404i) q^{86} +(-3.12512 + 3.12512i) q^{87} +(0.722857 - 4.80220i) q^{88} +(-4.91488 - 4.91488i) q^{89} +(-0.122630 + 2.46035i) q^{90} +(-3.22782 - 1.33701i) q^{91} +(1.27215 + 0.127130i) q^{92} +(3.56970 + 8.61802i) q^{93} +(-10.8694 - 5.15035i) q^{94} +7.49083 q^{95} +(1.39409 - 5.48238i) q^{96} -3.30926 q^{97} +(-8.05794 - 3.81817i) q^{98} +(-0.657053 - 1.58627i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} - 16 q^{12} - 32 q^{14} - 8 q^{16} - 8 q^{18} - 32 q^{20} - 8 q^{22} - 16 q^{23} - 8 q^{24} + 40 q^{26} + 40 q^{28} - 48 q^{31} + 40 q^{32} + 40 q^{34} - 48 q^{35} + 40 q^{38} + 8 q^{40} - 16 q^{43} + 8 q^{44} - 32 q^{46} + 24 q^{50} + 16 q^{51} - 8 q^{52} - 32 q^{53} + 8 q^{54} + 32 q^{55} + 56 q^{56} - 32 q^{58} + 64 q^{59} + 48 q^{60} - 32 q^{61} + 48 q^{62} + 16 q^{63} + 24 q^{64} + 48 q^{66} + 16 q^{67} - 8 q^{68} - 32 q^{69} - 24 q^{70} + 64 q^{71} - 32 q^{74} + 32 q^{75} - 56 q^{76} - 32 q^{77} + 24 q^{78} - 56 q^{80} - 40 q^{82} - 64 q^{86} - 48 q^{88} - 48 q^{91} - 80 q^{92} - 32 q^{94} - 40 q^{96} - 80 q^{98}+O(q^{100}) $ 32 * q - 8 * q^10 - 16 * q^12 - 32 * q^14 - 8 * q^16 - 8 * q^18 - 32 * q^20 - 8 * q^22 - 16 * q^23 - 8 * q^24 + 40 * q^26 + 40 * q^28 - 48 * q^31 + 40 * q^32 + 40 * q^34 - 48 * q^35 + 40 * q^38 + 8 * q^40 - 16 * q^43 + 8 * q^44 - 32 * q^46 + 24 * q^50 + 16 * q^51 - 8 * q^52 - 32 * q^53 + 8 * q^54 + 32 * q^55 + 56 * q^56 - 32 * q^58 + 64 * q^59 + 48 * q^60 - 32 * q^61 + 48 * q^62 + 16 * q^63 + 24 * q^64 + 48 * q^66 + 16 * q^67 - 8 * q^68 - 32 * q^69 - 24 * q^70 + 64 * q^71 - 32 * q^74 + 32 * q^75 - 56 * q^76 - 32 * q^77 + 24 * q^78 - 56 * q^80 - 40 * q^82 - 64 * q^86 - 48 * q^88 - 48 * q^91 - 80 * q^92 - 32 * q^94 - 40 * q^96 - 80 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/96\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$65$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.605567	−	1.27800i	0.428200	−	0.903684i
$2$	0.605567	−	1.27800i	0.428200	−	0.903684i
$3$	−0.382683	−	0.923880i	−0.220942	−	0.533402i
$3$	−0.382683	−	0.923880i	−0.220942	−	0.533402i
$4$	−1.26658	−	1.54783i	−0.633289	−	0.773916i
$5$	1.60930	+	0.666593i	0.719700	+	0.298109i	0.712312	−	0.701863i	$-0.247648\pi$
$5$	1.60930	+	0.666593i	0.719700	+	0.298109i	0.00738796	+	0.999973i	$0.497648\pi$
$6$	−1.41246	−	0.0704008i	−0.576634	−	0.0287410i
$7$	−0.589445	−	0.589445i	−0.222789	−	0.222789i	0.586883	−	0.809672i	$-0.300355\pi$
$7$	−0.589445	−	0.589445i	−0.222789	−	0.222789i	−0.809672	+	0.586883i	$0.800355\pi$
$8$	−2.74513	+	0.681373i	−0.970550	+	0.240902i
$9$	−0.707107	+	0.707107i	−0.235702	+	0.235702i
$10$	1.82644	−	1.65302i	0.577572	−	0.522730i
$11$	−0.657053	+	1.58627i	−0.198109	+	0.478277i	−0.991448	−	0.130503i	$-0.958341\pi$
$11$	−0.657053	+	1.58627i	−0.198109	+	0.478277i	0.793339	+	0.608780i	$0.208341\pi$
$12$	−0.945311	+	1.76249i	−0.272888	+	0.508788i
$13$	3.87213	−	1.60389i	1.07394	−	0.444839i	0.225558	−	0.974230i	$-0.427579\pi$
$13$	3.87213	−	1.60389i	1.07394	−	0.444839i	0.848378	+	0.529391i	$0.177579\pi$
$14$	−1.11026	+	0.396364i	−0.296730	+	0.105933i
$15$		−	1.74189i		−	0.449754i
$16$	−0.791564	+	3.92090i	−0.197891	+	0.980224i
$17$			7.96502i			1.93180i	0.258913	+	0.965901i	$0.416636\pi$
$17$			7.96502i			1.93180i	−0.258913	+	0.965901i	$0.583364\pi$
$18$	0.475483	+	1.33188i	0.112072	+	0.313928i
$19$	3.97306	−	1.64569i	0.911481	−	0.377548i	0.122858	−	0.992424i	$-0.460794\pi$
$19$	3.97306	−	1.64569i	0.911481	−	0.377548i	0.788624	+	0.614876i	$0.210794\pi$
$20$	−1.00653	−	3.33521i	−0.225066	−	0.745776i
$21$	−0.319006	+	0.770147i	−0.0696127	+	0.168060i
$22$	1.62936	+	1.80031i	0.347381	+	0.383827i
$23$	−0.452012	+	0.452012i	−0.0942511	+	0.0942511i	−0.752660	−	0.658409i	$-0.771230\pi$
$23$	−0.452012	+	0.452012i	−0.0942511	+	0.0942511i	0.658409	+	0.752660i	$0.271230\pi$
$24$	1.68002	+	2.27542i	0.342933	+	0.464468i
$25$	−1.39004	−	1.39004i	−0.278009	−	0.278009i
$26$	0.295061	−	5.91986i	0.0578663	−	1.16098i
$27$	0.923880	+	0.382683i	0.177801	+	0.0736475i
$28$	−0.165784	+	1.65894i	−0.0313302	+	0.313510i
$29$	−1.69130	−	4.08316i	−0.314067	−	0.758224i	−0.999546	−	0.0301318i	$-0.990407\pi$
$29$	−1.69130	−	4.08316i	−0.314067	−	0.758224i	0.685479	−	0.728092i	$-0.259593\pi$
$30$	−2.22614	−	1.05483i	−0.406436	−	0.192585i
$31$	−9.32808			−1.67537			−0.837686	−	0.546152i	$-0.816092\pi$
$31$	−9.32808			−1.67537			−0.837686	+	0.546152i	$0.816092\pi$
$32$	4.53157	+	3.38598i	0.801076	+	0.598563i
$33$	1.71696			0.298885
$34$	10.1793	+	4.82335i	1.74574	+	0.827198i
$35$	−0.555673	−	1.34151i	−0.0939258	−	0.226757i
$36$	1.99009	+	0.198877i	0.331681	+	0.0331461i
$37$	0.810329	+	0.335649i	0.133217	+	0.0551804i	0.448296	−	0.893885i	$-0.352031\pi$
$37$	0.810329	+	0.335649i	0.133217	+	0.0551804i	−0.315079	+	0.949065i	$0.602031\pi$
$38$	0.302752	−	6.07415i	0.0491128	−	0.985357i
$39$	−2.96360	−	2.96360i	−0.474556	−	0.474556i
$40$	−4.87193	−	0.733351i	−0.770319	−	0.115953i
$41$	−6.65023	+	6.65023i	−1.03859	+	1.03859i	−0.0393665	+	0.999225i	$0.512534\pi$
$41$	−6.65023	+	6.65023i	−1.03859	+	1.03859i	−0.999225	+	0.0393665i	$0.987466\pi$
$42$	0.791071	+	0.874066i	0.122065	+	0.134871i
$43$	−2.22413	+	5.36952i	−0.339176	+	0.818844i	0.658619	+	0.752477i	$0.271141\pi$
$43$	−2.22413	+	5.36952i	−0.339176	+	0.818844i	−0.997795	+	0.0663675i	$0.978859\pi$
$44$	3.28748	−	0.992122i	0.495607	−	0.149568i
$45$	−1.60930	+	0.666593i	−0.239900	+	0.0993698i
$46$	0.303949	+	0.851396i	0.0448148	+	0.125532i
$47$		−	8.50500i		−	1.24058i	−0.784372	−	0.620291i	$-0.787015\pi$
$47$		−	8.50500i		−	1.24058i	0.784372	−	0.620291i	$-0.212985\pi$
$48$	3.92535	−	0.769153i	0.566576	−	0.111018i
$49$		−	6.30511i		−	0.900730i
$50$	−2.61824	+	0.934713i	−0.370275	+	0.132188i
$51$	7.35872	−	3.04808i	1.03043	−	0.426817i
$52$	−7.38691	−	3.96196i	−1.02438	−	0.549425i
$53$	1.10759	−	2.67397i	0.152140	−	0.367298i	−0.829373	−	0.558696i	$-0.811302\pi$
$53$	1.10759	−	2.67397i	0.152140	−	0.367298i	0.981513	+	0.191398i	$0.0613020\pi$
$54$	1.04854	−	0.948979i	0.142688	−	0.129140i
$55$	−2.11479	+	2.11479i	−0.285158	+	0.285158i
$56$	2.01974	+	1.21647i	0.269898	+	0.162558i
$57$	−3.04084	−	3.04084i	−0.402770	−	0.402770i
$58$	−6.24248	−	0.311142i	−0.819678	−	0.0408549i
$59$	−1.92200	−	0.796118i	−0.250223	−	0.103646i	0.254047	−	0.967192i	$-0.418238\pi$
$59$	−1.92200	−	0.796118i	−0.250223	−	0.103646i	−0.504270	+	0.863546i	$0.668238\pi$
$60$	−2.69615	+	2.20624i	−0.348072	+	0.284824i
$61$	−4.70435	−	11.3573i	−0.602331	−	1.45416i	−0.871176	−	0.490972i	$-0.836642\pi$
$61$	−4.70435	−	11.3573i	−0.602331	−	1.45416i	0.268845	−	0.963183i	$-0.413358\pi$
$62$	−5.64878	+	11.9213i	−0.717395	+	1.51401i
$63$	0.833602			0.105024
$64$	7.07146	−	3.74091i	0.883933	−	0.467614i
$65$	7.30055			0.905522
$66$	1.03974	−	2.19428i	0.127983	−	0.270097i
$67$	4.54765	+	10.9790i	0.555583	+	1.34130i	0.913232	+	0.407441i	$0.133579\pi$
$67$	4.54765	+	10.9790i	0.555583	+	1.34130i	−0.357648	+	0.933856i	$0.616421\pi$
$68$	12.3285	−	10.0883i	1.49505	−	1.22339i
$69$	0.590582	+	0.244627i	0.0710978	+	0.0294497i
$70$	−2.05095	−	0.102225i	−0.245136	−	0.0122182i
$71$	9.09946	+	9.09946i	1.07991	+	1.07991i	0.996517	+	0.0833896i	$0.0265746\pi$
$71$	9.09946	+	9.09946i	1.07991	+	1.07991i	0.0833896	+	0.996517i	$0.473425\pi$
$72$	1.45930	−	2.42290i	0.171980	−	0.285542i
$73$	1.65052	−	1.65052i	0.193179	−	0.193179i	−0.603889	−	0.797068i	$-0.706383\pi$
$73$	1.65052	−	1.65052i	0.193179	−	0.193179i	0.797068	+	0.603889i	$0.206383\pi$
$74$	0.919668	−	0.832343i	0.106909	−	0.0967580i
$75$	−0.752286	+	1.81618i	−0.0868665	+	0.209714i
$76$	−7.57944	−	4.06522i	−0.869421	−	0.466313i
$77$	1.32231	−	0.547721i	0.150692	−	0.0624186i
$78$	−5.58215	+	1.99283i	−0.632054	+	0.225644i
$79$		−	0.580469i		−	0.0653079i	−0.999467	−	0.0326540i	$-0.989604\pi$
$79$		−	0.580469i		−	0.0653079i	0.999467	−	0.0326540i	$-0.0103959\pi$
$80$	−3.88750	+	5.78224i	−0.434636	+	0.646474i
$81$		−	1.00000i		−	0.111111i
$82$	4.47185	+	12.5262i	0.493833	+	1.38328i
$83$	3.33576	−	1.38172i	0.366147	−	0.151663i	−0.192021	−	0.981391i	$-0.561504\pi$
$83$	3.33576	−	1.38172i	0.366147	−	0.151663i	0.558168	+	0.829728i	$0.311504\pi$
$84$	1.59610	−	0.481685i	0.174149	−	0.0525561i
$85$	−5.30942	+	12.8181i	−0.575888	+	1.39032i
$86$	5.51540	+	6.09404i	0.594741	+	0.657138i
$87$	−3.12512	+	3.12512i	−0.335048	+	0.335048i
$88$	0.722857	−	4.80220i	0.0770568	−	0.511917i
$89$	−4.91488	−	4.91488i	−0.520976	−	0.520976i	0.396890	−	0.917866i	$-0.370089\pi$
$89$	−4.91488	−	4.91488i	−0.520976	−	0.520976i	−0.917866	+	0.396890i	$0.870089\pi$
$90$	−0.122630	+	2.46035i	−0.0129264	+	0.259344i
$91$	−3.22782	−	1.33701i	−0.338367	−	0.140156i
$92$	1.27215	+	0.127130i	0.132630	+	0.0132542i
$93$	3.56970	+	8.61802i	0.370161	+	0.893647i
$94$	−10.8694	−	5.15035i	−1.12109	−	0.531218i
$95$	7.49083			0.768543
$96$	1.39409	−	5.48238i	0.142283	−	0.559543i
$97$	−3.30926			−0.336005			−0.168002	−	0.985787i	$-0.553732\pi$
$97$	−3.30926			−0.336005			−0.168002	+	0.985787i	$0.553732\pi$
$98$	−8.05794	−	3.81817i	−0.813975	−	0.385693i
$99$	−0.657053	−	1.58627i	−0.0660363	−	0.159426i
$100$	−0.390955	+	3.91215i	−0.0390955	+	0.391215i
$101$	−2.59134	−	1.07337i	−0.257848	−	0.106804i	0.250015	−	0.968242i	$-0.419564\pi$
$101$	−2.59134	−	1.07337i	−0.257848	−	0.106804i	−0.507863	+	0.861438i	$0.669564\pi$
$102$	0.560744	−	11.2503i	0.0555219	−	1.11394i
$103$	12.7576	+	12.7576i	1.25705	+	1.25705i	0.952496	+	0.304550i	$0.0985061\pi$
$103$	12.7576	+	12.7576i	1.25705	+	1.25705i	0.304550	+	0.952496i	$0.401494\pi$
$104$	−9.53666	+	7.04125i	−0.935146	+	0.690451i
$105$	−1.02675	+	1.02675i	−0.100200	+	0.100200i
$106$	−2.74661	−	3.03477i	−0.266775	−	0.294763i
$107$	−3.17275	+	7.65969i	−0.306721	+	0.740490i	0.693086	+	0.720855i	$0.256250\pi$
$107$	−3.17275	+	7.65969i	−0.306721	+	0.740490i	−0.999807	+	0.0196351i	$0.993750\pi$
$108$	−0.577836	−	1.91471i	−0.0556022	−	0.184243i
$109$	10.8733	−	4.50386i	1.04147	−	0.431391i	0.204631	−	0.978839i	$-0.434401\pi$
$109$	10.8733	−	4.50386i	1.04147	−	0.431391i	0.836840	+	0.547448i	$0.184401\pi$
$110$	1.42206	+	3.98335i	0.135588	+	0.379797i
$111$		−	0.877093i		−	0.0832500i
$112$	2.77774	−	1.84457i	0.262472	−	0.174296i
$113$		−	1.05718i		−	0.0994515i	−0.998763	−	0.0497257i	$-0.984165\pi$
$113$		−	1.05718i		−	0.0994515i	0.998763	−	0.0497257i	$-0.0158347\pi$
$114$	−5.72764	+	2.04477i	−0.536443	+	0.191510i
$115$	−1.02873	+	0.426114i	−0.0959296	+	0.0397353i
$116$	−4.17788	+	7.78949i	−0.387907	+	0.723236i
$117$	−1.60389	+	3.87213i	−0.148280	+	0.357979i
$118$	−2.18134	+	1.97422i	−0.200809	+	0.181741i
$119$	4.69494	−	4.69494i	0.430385	−	0.430385i
$120$	1.18688	+	4.78171i	0.108347	+	0.436509i
$121$	5.69365	+	5.69365i	0.517605	+	0.517605i
$122$	−17.3635	−	0.865441i	−1.57201	−	0.0783534i
$123$	8.68894	+	3.59908i	0.783456	+	0.324518i
$124$	11.8147	+	14.4383i	1.06099	+	1.29660i
$125$	−4.64336	−	11.2101i	−0.415315	−	1.00266i
$126$	0.504802	−	1.06534i	0.0449713	−	0.0949084i
$127$	−7.93736			−0.704327			−0.352163	−	0.935939i	$-0.614554\pi$
$127$	−7.93736			−0.704327			−0.352163	+	0.935939i	$0.614554\pi$
$128$	−0.498648	−	11.3027i	−0.0440747	−	0.999028i
$129$	5.81193			0.511712
$130$	4.42097	−	9.33012i	0.387745	−	0.818306i
$131$	−7.20756	−	17.4006i	−0.629727	−	1.52030i	−0.839962	−	0.542645i	$-0.817423\pi$
$131$	−7.20756	−	17.4006i	−0.629727	−	1.52030i	0.210234	−	0.977651i	$-0.432577\pi$
$132$	−2.17467	−	2.65757i	−0.189280	−	0.231312i
$133$	−3.31195	−	1.37185i	−0.287182	−	0.118955i
$134$	16.7851	+	0.836613i	1.45001	+	0.0722723i
$135$	1.23170	+	1.23170i	0.106008	+	0.106008i
$136$	−5.42715	−	21.8650i	−0.465374	−	1.87491i
$137$	0.305733	−	0.305733i	0.0261205	−	0.0261205i	−0.693926	−	0.720046i	$-0.744120\pi$
$137$	0.305733	−	0.305733i	0.0261205	−	0.0261205i	0.720046	+	0.693926i	$0.244120\pi$
$138$	0.670271	−	0.606627i	0.0570573	−	0.0516395i
$139$	6.72200	−	16.2283i	0.570153	−	1.37647i	−0.331273	−	0.943535i	$-0.607478\pi$
$139$	6.72200	−	16.2283i	0.570153	−	1.37647i	0.901425	−	0.432935i	$-0.142522\pi$
$140$	−1.37263	+	2.55922i	−0.116009	+	0.216293i
$141$	−7.85759	+	3.25472i	−0.661729	+	0.274097i
$142$	17.1394	−	6.11879i	1.43831	−	0.513478i
$143$			7.19608i			0.601766i
$144$	−2.21277	−	3.33221i	−0.184398	−	0.277684i
$145$		−	7.69843i		−	0.639320i
$146$	−1.10987	−	3.10887i	−0.0918534	−	0.257292i
$147$	−5.82516	+	2.41286i	−0.480451	+	0.199009i
$148$	−0.506816	−	1.67938i	−0.0416600	−	0.138044i
$149$	2.14465	−	5.17765i	0.175697	−	0.424170i	−0.811359	−	0.584549i	$-0.801272\pi$
$149$	2.14465	−	5.17765i	0.175697	−	0.424170i	0.987056	+	0.160379i	$0.0512716\pi$
$150$	1.86552	+	2.06124i	0.152319	+	0.168300i
$151$	10.2384	−	10.2384i	0.833193	−	0.833193i	−0.154759	−	0.987952i	$-0.549460\pi$
$151$	10.2384	−	10.2384i	0.833193	−	0.833193i	0.987952	+	0.154759i	$0.0494603\pi$
$152$	−9.78522	+	7.22477i	−0.793686	+	0.586006i
$153$	−5.63212	−	5.63212i	−0.455330	−	0.455330i
$154$	0.100762	−	2.02160i	0.00811963	−	0.162905i
$155$	−15.0116	−	6.21803i	−1.20576	−	0.499444i
$156$	−0.833525	+	8.34079i	−0.0667354	+	0.667797i
$157$	4.64097	+	11.2043i	0.370389	+	0.894199i	0.993684	+	0.112212i	$0.0357936\pi$
$157$	4.64097	+	11.2043i	0.370389	+	0.894199i	−0.623295	+	0.781987i	$0.714206\pi$
$158$	−0.741841	−	0.351513i	−0.0590177	−	0.0279649i
$159$	−2.89428			−0.229532
$160$	5.03557	+	8.46977i	0.398096	+	0.669594i
$161$	0.532873			0.0419963
$162$	−1.27800	−	0.605567i	−0.100409	−	0.0475778i
$163$	0.981891	+	2.37049i	0.0769076	+	0.185671i	0.957657	−	0.287911i	$-0.0929607\pi$
$163$	0.981891	+	2.37049i	0.0769076	+	0.185671i	−0.880750	+	0.473582i	$0.842961\pi$
$164$	18.7165	+	1.87040i	1.46151	+	0.146054i
$165$	2.76310	+	1.14451i	0.215107	+	0.0891004i
$166$	0.254189	−	5.09983i	0.0197289	−	0.395823i
$167$	−6.83087	−	6.83087i	−0.528588	−	0.528588i	0.391563	−	0.920151i	$-0.371934\pi$
$167$	−6.83087	−	6.83087i	−0.528588	−	0.528588i	−0.920151	+	0.391563i	$0.871934\pi$
$168$	0.350954	−	2.33152i	0.0270767	−	0.179880i
$169$	3.22856	−	3.22856i	0.248351	−	0.248351i
$170$	13.1663	+	14.5477i	1.00981	+	1.11575i
$171$	−1.64569	+	3.97306i	−0.125849	+	0.303827i
$172$	11.1281	−	3.35834i	0.848513	−	0.256071i
$173$	2.76667	−	1.14599i	0.210346	−	0.0871282i	−0.275023	−	0.961438i	$-0.588685\pi$
$173$	2.76667	−	1.14599i	0.210346	−	0.0871282i	0.485369	+	0.874310i	$0.338685\pi$
$174$	2.10144	+	5.88637i	0.159310	+	0.446245i
$175$			1.63871i			0.123875i
$176$	−5.69949	−	3.83187i	−0.429615	−	0.288838i
$177$			2.08036i			0.156369i
$178$	−9.25751	+	3.30494i	−0.693880	+	0.247715i
$179$	−13.3854	+	5.54441i	−1.00047	+	0.414409i	−0.821970	−	0.569531i	$-0.807125\pi$
$179$	−13.3854	+	5.54441i	−1.00047	+	0.414409i	−0.178501	+	0.983940i	$0.557125\pi$
$180$	3.07007	+	1.64663i	0.228830	+	0.122732i
$181$	−9.03488	+	21.8121i	−0.671557	+	1.62128i	0.107407	+	0.994215i	$0.465745\pi$
$181$	−9.03488	+	21.8121i	−0.671557	+	1.62128i	−0.778965	+	0.627068i	$0.784255\pi$
$182$	−3.66335	+	3.31551i	−0.271546	+	0.245762i
$183$	−8.69251	+	8.69251i	−0.642569	+	0.642569i
$184$	0.932843	−	1.54882i	0.0687701	−	0.114181i
$185$	1.08032	+	1.08032i	0.0794266	+	0.0794266i
$186$	13.1755	+	0.656704i	0.966077	+	0.0481519i
$187$	−12.6346	−	5.23344i	−0.923937	−	0.382707i
$188$	−13.1643	+	10.7722i	−0.960105	+	0.785646i
$189$	−0.319006	−	0.770147i	−0.0232042	−	0.0560200i
$190$	4.53620	−	9.57330i	0.329091	−	0.694520i
$191$	15.9720			1.15570			0.577848	−	0.816144i	$-0.303893\pi$
$191$	15.9720			1.15570			0.577848	+	0.816144i	$0.303893\pi$
$192$	−6.16228	−	5.10159i	−0.444724	−	0.368176i
$193$	0.411129			0.0295937			0.0147968	−	0.999891i	$-0.495290\pi$
$193$	0.411129			0.0295937			0.0147968	+	0.999891i	$0.495290\pi$
$194$	−2.00398	+	4.22924i	−0.143877	+	0.303642i
$195$	−2.79380	−	6.74483i	−0.200068	−	0.483007i
$196$	−9.75924	+	7.98591i	−0.697089	+	0.570422i
$197$	−4.09727	−	1.69715i	−0.291919	−	0.120917i	0.231918	−	0.972735i	$-0.425500\pi$
$197$	−4.09727	−	1.69715i	−0.291919	−	0.120917i	−0.523837	+	0.851819i	$0.675500\pi$
$198$	−2.42514	−	0.120876i	−0.172347	−	0.00859025i
$199$	−8.65705	−	8.65705i	−0.613682	−	0.613682i	0.330221	−	0.943904i	$-0.392877\pi$
$199$	−8.65705	−	8.65705i	−0.613682	−	0.613682i	−0.943904	+	0.330221i	$0.892877\pi$
$200$	4.76298	+	2.86871i	0.336794	+	0.202848i
$201$	8.40296	−	8.40296i	0.592699	−	0.592699i
$202$	−2.94100	+	2.66174i	−0.206928	+	0.187280i
$203$	−1.40987	+	3.40373i	−0.0989535	+	0.238895i
$204$	−14.0383	−	7.52943i	−0.982878	−	0.527165i
$205$	−15.1352	+	6.26920i	−1.05709	+	0.437860i
$206$	24.0299	−	8.57867i	1.67424	−	0.597705i
$207$		−	0.639242i		−	0.0444304i
$208$	3.22365	+	16.4518i	0.223520	+	1.14073i
$209$			7.38363i			0.510737i
$210$	0.690422	+	1.93395i	0.0476436	+	0.133455i
$211$	−4.51505	+	1.87019i	−0.310829	+	0.128749i	−0.532644	−	0.846339i	$-0.678802\pi$
$211$	−4.51505	+	1.87019i	−0.310829	+	0.128749i	0.221816	+	0.975089i	$0.428802\pi$
$212$	−5.54171	+	1.67242i	−0.380606	+	0.114862i
$213$	4.92459	−	11.8890i	0.337427	−	0.814622i
$214$	7.86778	+	8.69323i	0.537831	+	0.594257i
$215$	−7.15857	+	7.15857i	−0.488210	+	0.488210i
$216$	−2.79692	−	0.421009i	−0.190306	−	0.0286460i
$217$	5.49839	+	5.49839i	0.373255	+	0.373255i
$218$	0.828557	−	16.6234i	0.0561170	−	1.12588i
$219$	−2.15651	−	0.893256i	−0.145723	−	0.0603606i
$220$	5.95188	+	0.594792i	0.401275	+	0.0401009i
$221$	12.7750	+	30.8416i	0.859341	+	2.07463i
$222$	−1.12093	−	0.531139i	−0.0752317	−	0.0356477i
$223$	−8.07183			−0.540530			−0.270265	−	0.962786i	$-0.587111\pi$
$223$	−8.07183			−0.540530			−0.270265	+	0.962786i	$0.587111\pi$
$224$	−0.675259	−	4.66696i	−0.0451176	−	0.311825i
$225$	1.96582			0.131054
$226$	−1.35108	−	0.640196i	−0.0898727	−	0.0425852i
$227$	−0.993337	−	2.39813i	−0.0659301	−	0.159169i	0.887480	−	0.460846i	$-0.152454\pi$
$227$	−0.993337	−	2.39813i	−0.0659301	−	0.159169i	−0.953410	+	0.301676i	$0.902454\pi$
$228$	−0.855250	+	8.55818i	−0.0566403	+	0.566779i
$229$	9.46203	+	3.91930i	0.625269	+	0.258995i	0.672741	−	0.739878i	$-0.265117\pi$
$229$	9.46203	+	3.91930i	0.625269	+	0.258995i	−0.0474727	+	0.998873i	$0.515117\pi$
$230$	−0.0783905	+	1.57276i	−0.00516892	+	0.103705i
$231$	−1.01206	−	1.01206i	−0.0665884	−	0.0665884i
$232$	7.42499	+	10.0564i	0.487475	+	0.660235i
$233$	5.94847	−	5.94847i	0.389698	−	0.389698i	−0.484882	−	0.874580i	$-0.661137\pi$
$233$	5.94847	−	5.94847i	0.389698	−	0.389698i	0.874580	+	0.484882i	$0.161137\pi$
$234$	3.97733	+	4.39461i	0.260006	+	0.287285i
$235$	5.66937	−	13.6871i	0.369829	−	0.892846i
$236$	1.20210	+	3.98327i	0.0782503	+	0.259289i
$237$	−0.536284	+	0.222136i	−0.0348354	+	0.0144293i
$238$	−3.15704	−	8.84325i	−0.204641	−	0.573223i
$239$			2.07158i			0.134000i	0.997753	+	0.0669998i	$0.0213427\pi$
$239$			2.07158i			0.134000i	−0.997753	+	0.0669998i	$0.978657\pi$
$240$	6.82977	+	1.37882i	0.440860	+	0.0890023i
$241$		−	5.10031i		−	0.328540i	−0.986415	−	0.164270i	$-0.947473\pi$
$241$		−	5.10031i		−	0.328540i	0.986415	−	0.164270i	$-0.0525268\pi$
$242$	10.7244	−	3.82861i	0.689389	−	0.246112i
$243$	−0.923880	+	0.382683i	−0.0592669	+	0.0245492i
$244$	−11.6208	+	21.6665i	−0.743944	+	1.38705i
$245$	4.20294	−	10.1468i	0.268516	−	0.648255i
$246$	9.86137	−	8.92500i	0.628738	−	0.569037i
$247$	12.7447	−	12.7447i	0.810925	−	0.810925i
$248$	25.6068	−	6.35590i	1.62603	−	0.403600i
$249$	−2.55308	−	2.55308i	−0.161795	−	0.161795i
$250$	−17.1384	−	0.854221i	−1.08392	−	0.0540257i
$251$	15.6741	+	6.49243i	0.989341	+	0.409798i	0.817878	−	0.575392i	$-0.195151\pi$
$251$	15.6741	+	6.49243i	0.989341	+	0.409798i	0.171463	+	0.985191i	$0.445151\pi$
$252$	−1.05582	−	1.29027i	−0.0665105	−	0.0812797i
$253$	−0.420016	−	1.01401i	−0.0264062	−	0.0637501i
$254$	−4.80660	+	10.1440i	−0.301593	+	0.636489i
$255$	13.8742			0.868836
$256$	−14.7469	−	6.20728i	−0.921678	−	0.387955i
$257$	12.7920			0.797942			0.398971	−	0.916964i	$-0.369367\pi$
$257$	12.7920			0.797942			0.398971	+	0.916964i	$0.369367\pi$
$258$	3.51951	−	7.42765i	0.219115	−	0.462425i
$259$	−0.279798	−	0.675491i	−0.0173858	−	0.0419730i
$260$	−9.24672	−	11.3000i	−0.573457	−	0.700798i
$261$	4.08316	+	1.69130i	0.252741	+	0.104689i
$262$	−26.6026	−	1.32595i	−1.64352	−	0.0819172i
$263$	−5.06752	−	5.06752i	−0.312477	−	0.312477i	0.533392	−	0.845868i	$-0.320917\pi$
$263$	−5.06752	−	5.06752i	−0.312477	−	0.312477i	−0.845868	+	0.533392i	$0.820917\pi$
$264$	−4.71328	+	1.16989i	−0.290083	+	0.0720019i
$265$	3.56490	−	3.56490i	0.218990	−	0.218990i
$266$	−3.75883	+	3.40192i	−0.230469	+	0.208585i
$267$	−2.65991	+	6.42160i	−0.162784	+	0.392995i
$268$	11.2337	−	20.9447i	0.686206	−	1.27940i
$269$	−16.4527	+	6.81494i	−1.00314	+	0.415514i	−0.822948	−	0.568117i	$-0.807672\pi$
$269$	−16.4527	+	6.81494i	−1.00314	+	0.415514i	−0.180192	+	0.983631i	$0.557672\pi$
$270$	2.32000	−	0.828240i	0.141190	−	0.0504051i
$271$			6.40145i			0.388860i	0.980916	+	0.194430i	$0.0622857\pi$
$271$			6.40145i			0.388860i	−0.980916	+	0.194430i	$0.937714\pi$
$272$	−31.2300	−	6.30482i	−1.89360	−	0.382286i
$273$			3.49376i			0.211452i
$274$	−0.205586	−	0.575869i	−0.0124199	−	0.0347895i
$275$	3.11831	−	1.29165i	0.188041	−	0.0778892i
$276$	−0.369377	−	1.22396i	−0.0222339	−	0.0736738i
$277$	2.00777	−	4.84718i	0.120635	−	0.291239i	−0.852014	−	0.523519i	$-0.824619\pi$
$277$	2.00777	−	4.84718i	0.120635	−	0.291239i	0.972649	+	0.232281i	$0.0746187\pi$
$278$	−16.6692	−	18.4181i	−0.999754	−	1.10464i
$279$	6.59595	−	6.59595i	0.394889	−	0.394889i
$280$	2.43946	+	3.30400i	0.145786	+	0.197452i
$281$	9.02739	+	9.02739i	0.538529	+	0.538529i	0.923097	−	0.384568i	$-0.125649\pi$
$281$	9.02739	+	9.02739i	0.538529	+	0.538529i	−0.384568	+	0.923097i	$0.625649\pi$
$282$	−0.598758	+	12.0130i	−0.0356555	+	0.715362i
$283$	7.91426	+	3.27819i	0.470454	+	0.194868i	0.605299	−	0.795998i	$-0.293054\pi$
$283$	7.91426	+	3.27819i	0.470454	+	0.194868i	−0.134845	+	0.990867i	$0.543054\pi$
$284$	2.55926	−	25.6096i	0.151864	−	1.51965i
$285$	−2.86662	−	6.92063i	−0.169804	−	0.409943i
$286$	9.19660	+	4.35771i	0.543806	+	0.257677i
$287$	7.83989			0.462774
$288$	−5.59856	+	0.810050i	−0.329898	+	0.0477326i
$289$	−46.4416			−2.73186
$290$	−9.83860	−	4.66191i	−0.577743	−	0.273757i
$291$	1.26640	+	3.05736i	0.0742377	+	0.179226i
$292$	−4.64524	−	0.464216i	−0.271842	−	0.0271662i
$293$	−1.10609	−	0.458156i	−0.0646183	−	0.0267658i	0.350140	−	0.936697i	$-0.386134\pi$
$293$	−1.10609	−	0.458156i	−0.0646183	−	0.0267658i	−0.414758	+	0.909932i	$0.636134\pi$
$294$	−0.443884	+	8.90571i	−0.0258879	+	0.519392i
$295$	−2.56238	−	2.56238i	−0.149188	−	0.149188i
$296$	−2.45316	−	0.369264i	−0.142587	−	0.0214630i
$297$	−1.21408	+	1.21408i	−0.0704478	+	0.0704478i
$298$	−5.31832	−	5.87628i	−0.308082	−	0.340404i
$299$	−1.02527	+	2.47523i	−0.0592931	+	0.143146i
$300$	3.76397	−	1.13592i	0.217313	−	0.0655823i
$301$	4.47604	−	1.85404i	0.257995	−	0.106865i
$302$	−6.88469	−	19.2848i	−0.396169	−	1.10972i
$303$			2.80485i			0.161134i
$304$	3.30767	+	16.8806i	0.189708	+	0.968169i
$305$		−	21.4132i		−	1.22612i
$306$	−10.6085	+	3.78723i	−0.606447	+	0.216502i
$307$	10.0335	−	4.15602i	0.572643	−	0.237197i	−0.0775205	−	0.996991i	$-0.524700\pi$
$307$	10.0335	−	4.15602i	0.572643	−	0.237197i	0.650164	+	0.759794i	$0.274700\pi$
$308$	−2.52259	−	1.35299i	−0.143738	−	0.0770937i
$309$	6.90438	−	16.6686i	0.392776	−	0.948246i
$310$	−17.0372	+	15.4195i	−0.967649	+	0.875768i
$311$	−11.1912	+	11.1912i	−0.634595	+	0.634595i	−0.949217	−	0.314622i	$-0.898122\pi$
$311$	−11.1912	+	11.1912i	−0.634595	+	0.634595i	0.314622	+	0.949217i	$0.398122\pi$
$312$	10.1548	+	6.11615i	0.574902	+	0.346259i
$313$	15.1491	+	15.1491i	0.856279	+	0.856279i	0.990897	−	0.134619i	$-0.0429809\pi$
$313$	15.1491	+	15.1491i	0.856279	+	0.856279i	−0.134619	+	0.990897i	$0.542981\pi$
$314$	17.1295	+	0.853780i	0.966674	+	0.0481816i
$315$	1.34151	+	0.555673i	0.0755857	+	0.0313086i
$316$	−0.898469	+	0.735209i	−0.0505428	+	0.0413588i
$317$	−2.50910	−	6.05751i	−0.140925	−	0.340223i	0.837621	−	0.546252i	$-0.183946\pi$
$317$	−2.50910	−	6.05751i	−0.140925	−	0.340223i	−0.978546	+	0.206029i	$0.933946\pi$
$318$	−1.75268	+	3.69890i	−0.0982855	+	0.207424i
$319$	7.58826			0.424861
$320$	13.8737	−	1.30645i	0.775566	−	0.0730329i
$321$	8.29078			0.462746
$322$	0.322690	−	0.681013i	0.0179828	−	0.0379514i
$323$	13.1080	+	31.6455i	0.729348	+	1.76080i
$324$	−1.54783	+	1.26658i	−0.0859906	+	0.0703654i
$325$	−7.61191	−	3.15295i	−0.422233	−	0.174894i
$326$	3.62410	+	0.180635i	0.200720	+	0.0100044i
$327$	−8.32204	−	8.32204i	−0.460210	−	0.460210i
$328$	13.7245	−	22.7870i	0.757806	−	1.25820i
$329$	−5.01323	+	5.01323i	−0.276388	+	0.276388i
$330$	3.13594	−	2.83817i	0.172628	−	0.156236i
$331$	7.52873	−	18.1760i	0.413817	−	0.999042i	−0.570287	−	0.821446i	$-0.693168\pi$
$331$	7.52873	−	18.1760i	0.413817	−	0.999042i	0.984103	−	0.177596i	$-0.0568321\pi$
$332$	−6.36366	−	3.41314i	−0.349251	−	0.187320i
$333$	−0.810329	+	0.335649i	−0.0444057	+	0.0183935i
$334$	−12.8664	+	4.59331i	−0.704018	+	0.251335i
$335$			20.6999i			1.13096i
$336$	−2.76716	−	1.86041i	−0.150961	−	0.101494i
$337$			29.9155i			1.62960i	0.579741	+	0.814801i	$0.303154\pi$
$337$			29.9155i			1.62960i	−0.579741	+	0.814801i	$0.696846\pi$
$338$	−2.17100	−	6.08122i	−0.118087	−	0.330775i
$339$	−0.976711	+	0.404567i	−0.0530476	+	0.0219731i
$340$	26.5650	−	8.01700i	1.44069	−	0.434783i
$341$	6.12904	−	14.7968i	0.331906	−	0.801293i
$342$	4.08099	+	4.50915i	0.220675	+	0.243827i
$343$	−7.84263	+	7.84263i	−0.423462	+	0.423462i
$344$	2.44687	−	16.2555i	0.131927	−	0.876437i
$345$	0.787356	+	0.787356i	0.0423898	+	0.0423898i
$346$	0.210824	−	4.22978i	0.0113340	−	0.227395i
$347$	18.9783	+	7.86106i	1.01881	+	0.422004i	0.828660	−	0.559752i	$-0.189103\pi$
$347$	18.9783	+	7.86106i	1.01881	+	0.422004i	0.190147	+	0.981756i	$0.439103\pi$
$348$	8.79535	+	0.878951i	0.471480	+	0.0471167i
$349$	−2.93498	−	7.08568i	−0.157106	−	0.379288i	0.825653	−	0.564178i	$-0.190807\pi$
$349$	−2.93498	−	7.08568i	−0.157106	−	0.379288i	−0.982759	+	0.184891i	$0.940807\pi$
$350$	2.09427	+	0.992348i	0.111944	+	0.0530432i
$351$	4.19117			0.223708
$352$	−8.34856	+	4.96350i	−0.444980	+	0.264556i
$353$	−28.6693			−1.52591			−0.762956	−	0.646450i	$-0.776253\pi$
$353$	−28.6693			−1.52591			−0.762956	+	0.646450i	$0.776253\pi$
$354$	2.65870	+	1.25979i	0.141308	+	0.0669573i
$355$	8.57810	+	20.7094i	0.455278	+	1.09914i
$356$	−1.38233	+	13.8325i	−0.0732633	+	0.733120i
$357$	−6.13424	−	2.54089i	−0.324658	−	0.134478i
$358$	−1.01998	+	20.4641i	−0.0539078	+	1.08156i
$359$	−13.9965	−	13.9965i	−0.738709	−	0.738709i	0.233619	−	0.972328i	$-0.424943\pi$
$359$	−13.9965	−	13.9965i	−0.738709	−	0.738709i	−0.972328	+	0.233619i	$0.924943\pi$
$360$	3.96353	−	2.92641i	0.208896	−	0.154236i
$361$	−0.358168	+	0.358168i	−0.0188510	+	0.0188510i
$362$	22.4047	+	24.7553i	1.17757	+	1.30111i
$363$	3.08138	−	7.43911i	0.161731	−	0.390452i
$364$	2.01882	+	6.68954i	0.105815	+	0.350627i
$365$	3.75641	−	1.55595i	0.196619	−	0.0814424i
$366$	5.84515	+	16.3729i	0.305531	+	0.855827i
$367$		−	11.6706i		−	0.609203i	−0.952480	−	0.304601i	$-0.901477\pi$
$367$		−	11.6706i		−	0.609203i	0.952480	−	0.304601i	$-0.0985232\pi$
$368$	−1.41450	−	2.13009i	−0.0737357	−	0.111039i
$369$		−	9.40484i		−	0.489597i
$370$	2.03485	−	0.726444i	0.105787	−	0.0377660i
$371$	−2.22902	+	0.923292i	−0.115725	+	0.0479350i
$372$	8.81794	−	16.4407i	0.457189	−	0.852410i
$373$	10.5778	−	25.5370i	0.547697	−	1.32226i	−0.371491	−	0.928437i	$-0.621153\pi$
$373$	10.5778	−	25.5370i	0.547697	−	1.32226i	0.919187	−	0.393820i	$-0.128847\pi$
$374$	−14.3395	+	12.9779i	−0.741477	+	0.671071i
$375$	−8.57982	+	8.57982i	−0.443060	+	0.443060i
$376$	5.79507	+	23.3473i	0.298858	+	1.20405i
$377$	−13.0979	−	13.0979i	−0.674575	−	0.674575i
$378$	−1.17743	−	0.0586862i	−0.0605604	−	0.00301849i
$379$	11.2755	+	4.67048i	0.579185	+	0.239906i	0.652990	−	0.757366i	$-0.273514\pi$
$379$	11.2755	+	4.67048i	0.579185	+	0.239906i	−0.0738049	+	0.997273i	$0.523514\pi$
$380$	−9.48772	−	11.5945i	−0.486710	−	0.594788i
$381$	3.03750	+	7.33317i	0.155616	+	0.375689i
$382$	9.67214	−	20.4123i	0.494870	−	1.04438i
$383$	−14.2648			−0.728897			−0.364448	−	0.931224i	$-0.618742\pi$
$383$	−14.2648			−0.728897			−0.364448	+	0.931224i	$0.618742\pi$
$384$	−10.2515	+	4.78605i	−0.523146	+	0.244237i
$385$	2.49310			0.127060
$386$	0.248966	−	0.525423i	0.0126720	−	0.0267433i
$387$	−2.22413	−	5.36952i	−0.113059	−	0.272948i
$388$	4.19144	+	5.12218i	0.212788	+	0.260039i
$389$	16.9675	+	7.02815i	0.860284	+	0.356341i	0.768819	−	0.639467i	$-0.220845\pi$
$389$	16.9675	+	7.02815i	0.860284	+	0.356341i	0.0914656	+	0.995808i	$0.470845\pi$
$390$	−10.3117	−	0.513965i	−0.522155	−	0.0260256i
$391$	−3.60029	−	3.60029i	−0.182074	−	0.182074i
$392$	4.29613	+	17.3083i	0.216987	+	0.874203i
$393$	−13.3178	+	13.3178i	−0.671796	+	0.671796i
$394$	−4.65013	+	4.20859i	−0.234270	+	0.212026i
$395$	0.386937	−	0.934148i	0.0194689	−	0.0470021i
$396$	−1.62306	+	3.02614i	−0.0815621	+	0.152069i
$397$	12.7413	−	5.27761i	0.639466	−	0.264875i	−0.0393030	−	0.999227i	$-0.512514\pi$
$397$	12.7413	−	5.27761i	0.639466	−	0.264875i	0.678769	+	0.734352i	$0.262514\pi$
$398$	−16.3062	+	5.82131i	−0.817354	+	0.291796i
$399$			3.58482i			0.179466i
$400$	6.55052	−	4.34991i	0.327526	−	0.217495i
$401$			20.6525i			1.03134i	0.856788	+	0.515669i	$0.172457\pi$
$401$			20.6525i			1.03134i	−0.856788	+	0.515669i	$0.827543\pi$
$402$	−5.65044	−	15.8275i	−0.281818	−	0.789406i
$403$	−36.1196	+	14.9612i	−1.79924	+	0.745271i
$404$	1.62074	+	5.37047i	0.0806349	+	0.267191i
$405$	0.666593	−	1.60930i	0.0331233	−	0.0799666i
$406$	3.49620	+	3.86300i	0.173514	+	0.191718i
$407$	−1.06486	+	1.06486i	−0.0527831	+	0.0527831i
$408$	−18.1238	+	13.3814i	−0.897259	+	0.662478i
$409$	6.38072	+	6.38072i	0.315506	+	0.315506i	0.847038	−	0.531532i	$-0.178383\pi$
$409$	6.38072	+	6.38072i	0.315506	+	0.315506i	−0.531532	+	0.847038i	$0.678383\pi$
$410$	−1.15332	+	23.1392i	−0.0569584	+	1.14276i
$411$	−0.399459	−	0.165462i	−0.0197039	−	0.00816161i
$412$	3.58813	−	35.9052i	0.176775	−	1.76892i
$413$	0.663645	+	1.60218i	0.0326558	+	0.0788382i
$414$	−0.816952	−	0.387104i	−0.0401510	−	0.0190251i
$415$	6.28927			0.308728
$416$	22.9776	+	5.84285i	1.12657	+	0.286469i
$417$	−17.5654			−0.860183
$418$	9.43630	+	4.47128i	0.461544	+	0.218698i
$419$	−8.46204	−	20.4292i	−0.413398	−	0.998030i	−0.984219	−	0.176956i	$-0.943375\pi$
$419$	−8.46204	−	20.4292i	−0.413398	−	0.998030i	0.570821	−	0.821075i	$-0.306625\pi$
$420$	2.88969	+	0.288777i	0.141003	+	0.0140909i
$421$	−28.2742	−	11.7116i	−1.37800	−	0.570786i	−0.434054	−	0.900887i	$-0.642917\pi$
$421$	−28.2742	−	11.7116i	−1.37800	−	0.570786i	−0.943946	+	0.330100i	$0.892917\pi$
$422$	−0.344052	+	6.90277i	−0.0167482	+	0.336021i
$423$	6.01394	+	6.01394i	0.292408	+	0.292408i
$424$	−1.21852	+	8.09507i	−0.0591765	+	0.393132i
$425$	11.0717	−	11.0717i	0.537057	−	0.537057i
$426$	−12.2120	−	13.4932i	−0.591674	−	0.653749i
$427$	−3.92156	+	9.46748i	−0.189777	+	0.458163i
$428$	15.8744	−	4.79071i	0.767319	−	0.231568i
$429$	6.64831	−	2.75382i	0.320983	−	0.132956i
$430$	4.81367	+	13.4837i	0.232136	+	0.650239i
$431$			8.30038i			0.399815i	0.979815	+	0.199908i	$0.0640642\pi$
$431$			8.30038i			0.399815i	−0.979815	+	0.199908i	$0.935936\pi$
$432$	−2.23177	+	3.31952i	−0.107376	+	0.159710i
$433$		−	29.4261i		−	1.41413i	−0.707150	−	0.707063i	$-0.750020\pi$
$433$		−	29.4261i		−	1.41413i	0.707150	−	0.707063i	$-0.249980\pi$
$434$	10.3566	−	3.69731i	0.497133	−	0.177477i
$435$	−7.11242	+	2.94606i	−0.341014	+	0.141253i
$436$	−20.7431	−	11.1255i	−0.993412	−	0.532815i
$437$	−1.05200	+	2.53974i	−0.0503238	+	0.121492i
$438$	−2.44749	+	2.21510i	−0.116946	+	0.105841i
$439$	20.3138	−	20.3138i	0.969524	−	0.969524i	−0.0300252	−	0.999549i	$-0.509559\pi$
$439$	20.3138	−	20.3138i	0.969524	−	0.969524i	0.999549	+	0.0300252i	$0.00955876\pi$
$440$	4.36441	−	7.24632i	0.208065	−	0.345455i
$441$	4.45838	+	4.45838i	0.212304	+	0.212304i
$442$	47.1518	+	2.35017i	2.24278	+	0.111786i
$443$	18.1169	+	7.50428i	0.860762	+	0.356539i	0.769005	−	0.639242i	$-0.220752\pi$
$443$	18.1169	+	7.50428i	0.860762	+	0.356539i	0.0917565	+	0.995781i	$0.470752\pi$
$444$	−1.35759	+	1.11091i	−0.0644285	+	0.0527213i
$445$	−4.63328	−	11.1857i	−0.219638	−	0.530254i
$446$	−4.88803	+	10.3158i	−0.231455	+	0.488468i
$447$	−5.60425			−0.265072
$448$	−6.37330	−	1.96318i	−0.301110	−	0.0927514i
$449$	−8.20853			−0.387384			−0.193692	−	0.981062i	$-0.562046\pi$
$449$	−8.20853			−0.387384			−0.193692	+	0.981062i	$0.562046\pi$
$450$	1.19043	−	2.51232i	0.0561176	−	0.118432i
$451$	−6.17948	−	14.9186i	−0.290981	−	0.702489i
$452$	−1.63634	+	1.33901i	−0.0769671	+	0.0629815i
$453$	−13.3772	−	5.54101i	−0.628514	−	0.260339i
$454$	−3.66634	−	0.182740i	−0.172070	−	0.00857643i
$455$	−4.30328	−	4.30328i	−0.201741	−	0.201741i
$456$	10.4195	+	6.27556i	0.487936	+	0.293880i
$457$	−12.2056	+	12.2056i	−0.570953	+	0.570953i	−0.932395	−	0.361442i	$-0.882285\pi$
$457$	−12.2056	+	12.2056i	−0.570953	+	0.570953i	0.361442	+	0.932395i	$0.382285\pi$
$458$	10.7388	−	9.71909i	0.501790	−	0.454143i
$459$	−3.04808	+	7.35872i	−0.142272	+	0.343476i
$460$	1.96252	+	1.05259i	0.0915029	+	0.0490775i
$461$	−28.6007	+	11.8468i	−1.33207	+	0.551761i	−0.931245	−	0.364394i	$-0.881276\pi$
$461$	−28.6007	+	11.8468i	−1.33207	+	0.551761i	−0.400824	+	0.916155i	$0.631276\pi$
$462$	−1.90628	+	0.680542i	−0.0886880	+	0.0316617i
$463$			22.9354i			1.06590i	0.846148	+	0.532948i	$0.178916\pi$
$463$			22.9354i			1.06590i	−0.846148	+	0.532948i	$0.821084\pi$
$464$	17.3484	−	3.39933i	0.805380	−	0.157810i
$465$			16.2485i			0.753506i
$466$	−3.99996	−	11.2044i	−0.185295	−	0.519032i
$467$	20.6535	−	8.55495i	0.955729	−	0.395876i	0.150348	−	0.988633i	$-0.451961\pi$
$467$	20.6535	−	8.55495i	0.955729	−	0.395876i	0.805381	+	0.592757i	$0.201961\pi$
$468$	8.02486	−	2.42180i	0.370949	−	0.111948i
$469$	3.79093	−	9.15210i	0.175049	−	0.422605i
$470$	−14.0589	−	15.5339i	−0.648489	−	0.716525i
$471$	8.57539	−	8.57539i	0.395133	−	0.395133i
$472$	5.81859	+	0.875849i	0.267822	+	0.0403142i
$473$	−7.05612	−	7.05612i	−0.324441	−	0.324441i
$474$	−0.0408655	+	0.819890i	−0.00187701	+	0.0376588i
$475$	−7.81030	−	3.23513i	−0.358361	−	0.148438i
$476$	−13.2135	−	1.32047i	−0.605639	−	0.0605237i
$477$	1.10759	+	2.67397i	0.0507133	+	0.122433i
$478$	2.64749	+	1.25448i	0.121093	+	0.0573787i
$479$	−41.8313			−1.91132			−0.955661	−	0.294468i	$-0.904858\pi$
$479$	−41.8313			−1.91132			−0.955661	+	0.294468i	$0.904858\pi$
$480$	5.89801	−	7.89350i	0.269206	−	0.360287i
$481$	3.67604			0.167613
$482$	−6.51820	−	3.08858i	−0.296896	−	0.140681i
$483$	−0.203922	−	0.492310i	−0.00927876	−	0.0224009i
$484$	1.60136	−	16.0243i	0.0727892	−	0.728376i
$485$	−5.32559	−	2.20593i	−0.241822	−	0.100166i
$486$	−0.0704008	+	1.41246i	−0.00319344	+	0.0640705i
$487$	4.02796	+	4.02796i	0.182524	+	0.182524i	0.792455	−	0.609931i	$-0.208803\pi$
$487$	4.02796	+	4.02796i	0.182524	+	0.182524i	−0.609931	+	0.792455i	$0.708803\pi$
$488$	20.6526	+	27.9719i	0.934900	+	1.26623i
$489$	1.81430	−	1.81430i	0.0820454	−	0.0820454i
$490$	−10.4225	−	11.5159i	−0.470839	−	0.520236i
$491$	15.7614	−	38.0514i	0.711301	−	1.71723i	0.0145778	−	0.999894i	$-0.495360\pi$
$491$	15.7614	−	38.0514i	0.711301	−	1.71723i	0.696724	−	0.717340i	$-0.254640\pi$
$492$	−5.43445	−	18.0075i	−0.245004	−	0.811842i
$493$	32.5225	−	13.4712i	1.46474	−	0.606714i
$494$	−8.56997	−	24.0055i	−0.385581	−	1.08006i
$495$		−	2.99076i		−	0.134425i
$496$	7.38377	−	36.5744i	0.331541	−	1.64224i
$497$		−	10.7273i		−	0.481184i
$498$	−4.80890	+	1.71678i	−0.215492	+	0.0769308i
$499$	7.53276	−	3.12017i	0.337213	−	0.139678i	−0.207650	−	0.978203i	$-0.566582\pi$
$499$	7.53276	−	3.12017i	0.337213	−	0.139678i	0.544863	+	0.838525i	$0.316582\pi$
$500$	−11.4701	+	21.3856i	−0.512959	+	0.956391i
$501$	−3.69684	+	8.92496i	−0.165163	+	0.398738i
$502$	17.7891	−	16.0999i	0.793964	−	0.718575i
$503$	10.0612	−	10.0612i	0.448607	−	0.448607i	−0.446284	−	0.894891i	$-0.647253\pi$
$503$	10.0612	−	10.0612i	0.448607	−	0.448607i	0.894891	+	0.446284i	$0.147253\pi$
$504$	−2.28834	+	0.567993i	−0.101931	+	0.0253004i
$505$	−3.45474	−	3.45474i	−0.153734	−	0.153734i
$506$	−1.55025	−	0.0772687i	−0.0689171	−	0.00343501i
$507$	−4.21832	−	1.74728i	−0.187342	−	0.0775996i
$508$	10.0533	+	12.2857i	0.446042	+	0.545090i
$509$	5.89292	+	14.2268i	0.261199	+	0.630590i	0.999013	−	0.0444138i	$-0.0141420\pi$
$509$	5.89292	+	14.2268i	0.261199	+	0.630590i	−0.737814	+	0.675004i	$0.764142\pi$
$510$	8.40175	−	17.7312i	0.372036	−	0.785153i
$511$	−1.94578			−0.0860765
$512$	−16.8631	+	15.0876i	−0.745252	+	0.666783i
$513$	4.30040			0.189867
$514$	7.74640	−	16.3482i	0.341679	−	0.721087i
$515$	12.0267	+	29.0350i	0.529958	+	1.27943i
$516$	−7.36126	−	8.99588i	−0.324061	−	0.396022i
$517$	13.4912	+	5.58824i	0.593342	+	0.245770i
$518$	−1.03272	−	0.0514733i	−0.0453749	−	0.00226161i
$519$	−2.11752	−	2.11752i	−0.0929487	−	0.0929487i
$520$	−20.0410	+	4.97440i	−0.878854	+	0.218142i
$521$	11.9481	−	11.9481i	0.523456	−	0.523456i	−0.395158	−	0.918613i	$-0.629310\pi$
$521$	11.9481	−	11.9481i	0.523456	−	0.523456i	0.918613	+	0.395158i	$0.129310\pi$
$522$	4.63411	−	4.19409i	0.202830	−	0.183570i
$523$	−6.15336	+	14.8555i	−0.269068	+	0.649587i	−0.999440	−	0.0334625i	$-0.989347\pi$
$523$	−6.15336	+	14.8555i	−0.269068	+	0.649587i	0.730372	+	0.683049i	$0.239347\pi$
$524$	−17.8042	+	33.1953i	−0.777782	+	1.45014i
$525$	1.51397	−	0.627107i	0.0660750	−	0.0273692i
$526$	−9.54503	+	3.40758i	−0.416183	+	0.148577i
$527$		−	74.2983i		−	3.23649i
$528$	−1.35909	+	6.73203i	−0.0591466	+	0.292974i
$529$			22.5914i			0.982233i
$530$	−2.39716	−	6.71473i	−0.104126	−	0.291669i
$531$	1.92200	−	0.796118i	0.0834076	−	0.0345486i
$532$	2.07144	+	6.86389i	0.0898082	+	0.297587i
$533$	−15.0843	+	36.4168i	−0.653375	+	1.57739i
$534$	6.59606	+	7.28808i	0.285439	+	0.315386i
$535$	−10.2118	+	10.2118i	−0.441494	+	0.441494i
$536$	−19.9647	−	27.0401i	−0.862342	−	1.16795i
$537$	10.2447	+	10.2447i	0.442093	+	0.442093i
$538$	−1.25372	+	25.1535i	−0.0540516	+	1.08444i
$539$	10.0016	+	4.14279i	0.430799	+	0.178443i
$540$	0.346421	−	3.46651i	0.0149076	−	0.149175i
$541$	8.64537	+	20.8718i	0.371693	+	0.897347i	0.993464	+	0.114148i	$0.0364137\pi$
$541$	8.64537	+	20.8718i	0.371693	+	0.897347i	−0.621770	+	0.783200i	$0.713586\pi$
$542$	8.18106	+	3.87650i	0.351407	+	0.166510i
$543$	23.6093			1.01317
$544$	−26.9694	+	36.0940i	−1.15631	+	1.54752i
$545$	20.5006			0.878148
$546$	4.46504	+	2.11571i	0.191086	+	0.0905439i
$547$	10.1653	+	24.5412i	0.434637	+	1.04931i	0.977774	+	0.209662i	$0.0672363\pi$
$547$	10.1653	+	24.5412i	0.434637	+	1.04931i	−0.543137	+	0.839644i	$0.682764\pi$
$548$	−0.860458	−	0.0859886i	−0.0367569	−	0.00367325i
$549$	11.3573	+	4.70435i	0.484718	+	0.200777i
$550$	0.237619	−	4.76738i	0.0101321	−	0.203282i
$551$	−13.4393	−	13.4393i	−0.572532	−	0.572532i
$552$	−1.78791	−	0.269126i	−0.0760984	−	0.0114548i
$553$	−0.342155	+	0.342155i	−0.0145499	+	0.0145499i
$554$	−4.97887	−	5.50122i	−0.211532	−	0.233725i
$555$	0.584664	−	1.41150i	0.0248176	−	0.0599150i
$556$	−33.6327	+	10.1499i	−1.42634	+	0.430453i
$557$	40.0425	−	16.5861i	1.69666	−	0.702778i	0.696761	−	0.717303i	$-0.254624\pi$
$557$	40.0425	−	16.5861i	1.69666	−	0.702778i	0.999894	+	0.0145256i	$0.00462381\pi$
$558$	−4.43535	−	12.4239i	−0.187763	−	0.525947i
$559$			24.3588i			1.03027i
$560$	5.69978	−	1.11684i	0.240860	−	0.0471952i
$561$			13.6756i			0.577386i
$562$	17.0037	−	6.07034i	0.717259	−	0.256062i
$563$	−18.6724	+	7.73435i	−0.786947	+	0.325964i	−0.739715	−	0.672920i	$-0.765040\pi$
$563$	−18.6724	+	7.73435i	−0.786947	+	0.325964i	−0.0472316	+	0.998884i	$0.515040\pi$
$564$	14.9900	+	8.03987i	0.631193	+	0.338540i
$565$	0.704711	−	1.70132i	0.0296474	−	0.0715752i
$566$	8.98215	−	8.12927i	0.377548	−	0.341699i
$567$	−0.589445	+	0.589445i	−0.0247544	+	0.0247544i
$568$	−31.1793	−	18.7791i	−1.30825	−	0.787952i
$569$	8.77986	+	8.77986i	0.368071	+	0.368071i	0.866773	−	0.498702i	$-0.166190\pi$
$569$	8.77986	+	8.77986i	0.368071	+	0.368071i	−0.498702	+	0.866773i	$0.666190\pi$
$570$	−10.5805	−	0.527360i	−0.443169	−	0.0220887i
$571$	−23.2136	−	9.61539i	−0.971459	−	0.402392i	−0.160204	−	0.987084i	$-0.551215\pi$
$571$	−23.2136	−	9.61539i	−0.971459	−	0.402392i	−0.811255	+	0.584692i	$0.801215\pi$
$572$	11.1383	−	9.11439i	0.465716	−	0.381092i
$573$	−6.11224	−	14.7562i	−0.255342	−	0.616451i
$574$	4.74758	−	10.0194i	0.198160	−	0.418202i
$575$	1.25663			0.0524052
$576$	−2.35506	+	7.64550i	−0.0981273	+	0.318563i
$577$	32.9671			1.37244			0.686220	−	0.727394i	$-0.259269\pi$
$577$	32.9671			1.37244			0.686220	+	0.727394i	$0.259269\pi$
$578$	−28.1235	+	59.3524i	−1.16978	+	2.46873i
$579$	−0.157332	−	0.379833i	−0.00653850	−	0.0157853i
$580$	−11.9159	+	9.75065i	−0.494779	+	0.404874i
$581$	−2.78069	−	1.15180i	−0.115363	−	0.0477848i
$582$	4.67420	+	0.232975i	0.193752	+	0.00965711i
$583$	3.51388	+	3.51388i	0.145530	+	0.145530i
$584$	−3.40627	+	5.65552i	−0.140953	+	0.234027i
$585$	−5.16227	+	5.16227i	−0.213434	+	0.213434i
$586$	−1.25533	+	1.13614i	−0.0518574	+	0.0469334i
$587$	6.05934	−	14.6285i	0.250096	−	0.603785i	−0.748115	−	0.663569i	$-0.769041\pi$
$587$	6.05934	−	14.6285i	0.250096	−	0.603785i	0.998211	+	0.0597837i	$0.0190411\pi$
$588$	11.1127	+	5.96029i	0.458281	+	0.245798i
$589$	−37.0610	+	15.3512i	−1.52707	+	0.632533i
$590$	−4.82642	+	1.72303i	−0.198701	+	0.0709362i
$591$			4.43486i			0.182426i
$592$	−1.95747	+	2.91153i	−0.0804516	+	0.119663i
$593$		−	21.5942i		−	0.886767i	−0.896332	−	0.443384i	$-0.853778\pi$
$593$		−	21.5942i		−	0.886767i	0.896332	−	0.443384i	$-0.146222\pi$
$594$	0.816387	+	2.28680i	0.0334968	+	0.0938284i
$595$	10.6852	−	4.42595i	0.438050	−	0.181446i
$596$	−10.7305	+	3.23833i	−0.439538	+	0.132647i
$597$	−4.68516	+	11.3110i	−0.191751	+	0.462928i
$598$	2.54248	+	2.80922i	0.103970	+	0.114877i
$599$	−16.6522	+	16.6522i	−0.680392	+	0.680392i	−0.960089	−	0.279696i	$-0.909766\pi$
$599$	−16.6522	+	16.6522i	−0.680392	+	0.680392i	0.279696	+	0.960089i	$0.409766\pi$
$600$	0.827627	−	5.49823i	0.0337877	−	0.224464i
$601$	17.8090	+	17.8090i	0.726445	+	0.726445i	0.969910	−	0.243465i	$-0.0782840\pi$
$601$	17.8090	+	17.8090i	0.726445	+	0.726445i	−0.243465	+	0.969910i	$0.578284\pi$
$602$	0.341080	−	6.84313i	0.0139014	−	0.278905i
$603$	−10.9790	−	4.54765i	−0.447099	−	0.185194i
$604$	−28.8152	−	2.87960i	−1.17247	−	0.117169i
$605$	5.36743	+	12.9581i	0.218217	+	0.526823i
$606$	3.58460	+	1.69852i	0.145615	+	0.0689978i
$607$	−2.08575			−0.0846579			−0.0423289	−	0.999104i	$-0.513478\pi$
$607$	−2.08575			−0.0846579			−0.0423289	+	0.999104i	$0.513478\pi$
$608$	23.5765	+	5.99513i	0.956152	+	0.243135i
$609$	3.68417			0.149290
$610$	−27.3661	−	12.9671i	−1.10802	−	0.525023i
$611$	−13.6411	−	32.9325i	−0.551859	−	1.33231i
$612$	−1.58406	+	15.8511i	−0.0640317	+	0.640742i
$613$	23.3947	+	9.69039i	0.944902	+	0.391391i	0.801312	−	0.598246i	$-0.204135\pi$
$613$	23.3947	+	9.69039i	0.944902	+	0.391391i	0.143590	+	0.989637i	$0.454135\pi$
$614$	0.764567	−	15.3396i	0.0308554	−	0.619056i
$615$	11.5840	+	11.5840i	0.467111	+	0.467111i
$616$	−3.25672	+	2.40455i	−0.131217	+	0.0968822i
$617$	−3.94760	+	3.94760i	−0.158924	+	0.158924i	−0.782090	−	0.623166i	$-0.785846\pi$
$617$	−3.94760	+	3.94760i	−0.158924	+	0.158924i	0.623166	+	0.782090i	$0.285846\pi$
$618$	−17.1215	−	18.9178i	−0.688728	−	0.760985i
$619$	−13.7586	+	33.2161i	−0.553004	+	1.33507i	0.362208	+	0.932097i	$0.382023\pi$
$619$	−13.7586	+	33.2161i	−0.553004	+	1.33507i	−0.915212	+	0.402972i	$0.867977\pi$
$620$	9.38896	+	31.1111i	0.377070	+	1.24945i
$621$	−0.590582	+	0.244627i	−0.0236993	+	0.00981655i
$622$	7.52536	+	21.0794i	0.301740	+	0.845208i
$623$			5.79410i			0.232136i
$624$	13.9659	−	9.27410i	0.559082	−	0.371261i
$625$		−	11.3065i		−	0.452259i
$626$	28.5344	−	10.1868i	1.14046	−	0.407146i
$627$	6.82159	−	2.82559i	0.272428	−	0.112843i
$628$	11.4642	−	21.3745i	0.457471	−	0.852936i
$629$	−2.67345	+	6.45428i	−0.106598	+	0.257349i
$630$	1.52253	−	1.37796i	0.0606589	−	0.0548992i
$631$	−28.2524	+	28.2524i	−1.12471	+	1.12471i	−0.133687	+	0.991024i	$0.542682\pi$
$631$	−28.2524	+	28.2524i	−1.12471	+	1.12471i	−0.991024	+	0.133687i	$0.957318\pi$
$632$	0.395516	+	1.59346i	0.0157328	+	0.0633846i
$633$	3.45567	+	3.45567i	0.137350	+	0.137350i
$634$	−9.26093	−	0.461590i	−0.367799	−	0.0183321i
$635$	−12.7736	−	5.29099i	−0.506904	−	0.209966i
$636$	3.66583	+	4.47986i	0.145360	+	0.177638i
$637$	−10.1127	−	24.4142i	−0.400680	−	0.967326i
$638$	4.59520	−	9.69781i	0.181926	−	0.383940i
$639$	−12.8686			−0.509073
$640$	6.73183	−	18.5218i	0.266099	−	0.732139i
$641$	9.34587			0.369140			0.184570	−	0.982819i	$-0.440911\pi$
$641$	9.34587			0.369140			0.184570	+	0.982819i	$0.440911\pi$
$642$	5.02062	−	10.5956i	0.198148	−	0.418176i
$643$	−14.3013	−	34.5265i	−0.563989	−	1.36159i	−0.906551	−	0.422096i	$-0.861295\pi$
$643$	−14.3013	−	34.5265i	−0.563989	−	1.36159i	0.342562	−	0.939495i	$-0.388705\pi$
$644$	−0.674925	−	0.824798i	−0.0265958	−	0.0325016i
$645$	9.35312	+	3.87419i	0.368279	+	0.152546i
$646$	48.3807	+	2.41142i	1.90351	+	0.0948762i
$647$	29.8159	+	29.8159i	1.17218	+	1.17218i	0.981688	+	0.190496i	$0.0610097\pi$
$647$	29.8159	+	29.8159i	1.17218	+	1.17218i	0.190496	+	0.981688i	$0.438990\pi$
$648$	0.681373	+	2.74513i	0.0267668	+	0.107839i
$649$	2.52571	−	2.52571i	0.0991428	−	0.0991428i
$650$	−8.63900	+	7.81870i	−0.338849	+	0.306675i
$651$	2.97571	−	7.18400i	0.116627	−	0.281563i
$652$	2.42548	−	4.52222i	0.0949893	−	0.177104i
$653$	−30.3070	+	12.5536i	−1.18600	+	0.491259i	−0.886452	−	0.462821i	$-0.846837\pi$
$653$	−30.3070	+	12.5536i	−1.18600	+	0.491259i	−0.299552	+	0.954080i	$0.596837\pi$
$654$	−15.6751	+	5.59603i	−0.612946	+	0.218822i
$655$		−	32.8072i		−	1.28188i
$656$	−20.8108	−	31.3389i	−0.812524	−	1.22358i
$657$			2.33419i			0.0910654i
$658$	3.37107	+	9.44277i	0.131418	+	0.368117i
$659$	23.8281	−	9.86994i	0.928212	−	0.384478i	0.133212	−	0.991088i	$-0.457471\pi$
$659$	23.8281	−	9.86994i	0.928212	−	0.384478i	0.795000	+	0.606609i	$0.207471\pi$
$660$	−1.72817	−	5.72643i	−0.0672688	−	0.222901i
$661$	−1.40604	+	3.39448i	−0.0546886	+	0.132030i	−0.948862	−	0.315690i	$-0.897764\pi$
$661$	−1.40604	+	3.39448i	−0.0546886	+	0.132030i	0.894174	+	0.447720i	$0.147764\pi$
$662$	−18.6698	−	20.6285i	−0.725621	−	0.801750i
$663$	23.6052	−	23.6052i	0.916748	−	0.916748i
$664$	−8.21563	+	6.06589i	−0.318828	+	0.235402i
$665$	−4.41544	−	4.41544i	−0.171223	−	0.171223i
$666$	−0.0617480	+	1.23886i	−0.00239269	+	0.0480048i
$667$	2.61013	+	1.08115i	0.101065	+	0.0418623i
$668$	−1.92121	+	19.2248i	−0.0743338	+	0.743832i
$669$	3.08896	+	7.45740i	0.119426	+	0.288320i
$670$	26.4545	+	12.5352i	1.02203	+	0.484276i
$671$	21.1067			0.814817
$672$	−4.05330	+	2.40983i	−0.156360	+	0.0929611i
$673$	19.4796			0.750885			0.375442	−	0.926846i	$-0.377491\pi$
$673$	19.4796			0.750885			0.375442	+	0.926846i	$0.377491\pi$
$674$	38.2321	+	18.1158i	1.47264	+	0.697796i
$675$	−0.752286	−	1.81618i	−0.0289555	−	0.0699047i
$676$	−9.08649	−	0.908045i	−0.349480	−	0.0349248i
$677$	19.1189	+	7.91933i	0.734801	+	0.304364i	0.718523	−	0.695503i	$-0.244818\pi$
$677$	19.1189	+	7.91933i	0.734801	+	0.304364i	0.0162777	+	0.999868i	$0.494818\pi$
$678$	−0.0744266	+	1.49323i	−0.00285833	+	0.0573472i
$679$	1.95063	+	1.95063i	0.0748583	+	0.0748583i
$680$	5.84116	−	38.8050i	0.223998	−	1.48810i
$681$	−1.83545	+	1.83545i	−0.0703345	+	0.0703345i
$682$	−15.1988	−	16.7934i	−0.581993	−	0.643052i
$683$	−8.46056	+	20.4256i	−0.323734	+	0.781564i	0.675296	+	0.737547i	$0.264016\pi$
$683$	−8.46056	+	20.4256i	−0.323734	+	0.781564i	−0.999031	+	0.0440175i	$0.985984\pi$
$684$	8.23402	−	2.48493i	0.314836	−	0.0950135i
$685$	0.695815	−	0.288216i	0.0265857	−	0.0110122i
$686$	5.27366	+	14.7721i	0.201349	+	0.564003i
$687$		−	10.2416i		−	0.390743i
$688$	−19.2928	−	12.9709i	−0.735531	−	0.494511i
$689$		−	12.1304i		−	0.462132i
$690$	1.48304	−	0.529446i	0.0564583	−	0.0201556i
$691$	−14.6182	+	6.05507i	−0.556104	+	0.230346i	−0.642993	−	0.765872i	$-0.722307\pi$
$691$	−14.6182	+	6.05507i	−0.556104	+	0.230346i	0.0868889	+	0.996218i	$0.472307\pi$
$692$	−5.27800	−	2.83085i	−0.200640	−	0.107613i
$693$	−0.547721	+	1.32231i	−0.0208062	+	0.0502306i
$694$	21.5391	−	19.4939i	0.817612	−	0.739978i
$695$	21.6354	−	21.6354i	0.820677	−	0.820677i
$696$	6.44948	−	10.7082i	0.244467	−	0.405894i
$697$	−52.9692	−	52.9692i	−2.00635	−	2.00635i
$698$	−10.8328	−	0.539937i	−0.410029	−	0.0204369i
$699$	−7.77206	−	3.21929i	−0.293966	−	0.121765i
$700$	2.53644	−	2.07555i	0.0958686	−	0.0784485i
$701$	−9.53654	−	23.0232i	−0.360190	−	0.869576i	−0.995272	−	0.0971307i	$-0.969034\pi$
$701$	−9.53654	−	23.0232i	−0.360190	−	0.869576i	0.635082	−	0.772445i	$-0.280966\pi$
$702$	2.53803	−	5.35632i	0.0957918	−	0.202161i
$703$	3.77186			0.142258
$704$	1.28776	+	13.6752i	0.0485342	+	0.515404i
$705$	−14.8148			−0.557957
$706$	−17.3612	+	36.6394i	−0.653396	+	1.37894i
$707$	0.894763	+	2.16015i	0.0336510	+	0.0812407i
$708$	3.22004	−	2.63493i	0.121017	−	0.0990268i
$709$	−4.53151	−	1.87701i	−0.170184	−	0.0704927i	0.295965	−	0.955199i	$-0.404359\pi$
$709$	−4.53151	−	1.87701i	−0.170184	−	0.0704927i	−0.466149	+	0.884706i	$0.654359\pi$
$710$	31.6612	+	1.57808i	1.18822	+	0.0592242i
$711$	0.410454	+	0.410454i	0.0153932	+	0.0153932i
$712$	16.8408	+	10.1431i	0.631137	+	0.380129i
$713$	4.21641	−	4.21641i	0.157906	−	0.157906i
$714$	−6.96195	+	6.30089i	−0.260544	+	0.235805i
$715$	−4.79685	+	11.5806i	−0.179392	+	0.433091i
$716$	25.5354	+	13.6959i	0.954304	+	0.511840i
$717$	1.91389	−	0.792761i	0.0714757	−	0.0296062i
$718$	−26.3634	+	9.41176i	−0.983875	+	0.351244i
$719$			39.7315i			1.48173i	0.671652	+	0.740867i	$0.265585\pi$
$719$			39.7315i			1.48173i	−0.671652	+	0.740867i	$0.734415\pi$
$720$	−1.33978	−	6.83754i	−0.0499306	−	0.254820i
$721$		−	15.0398i		−	0.560113i
$722$	0.240845	+	0.674634i	0.00896332	+	0.0251073i
$723$	−4.71207	+	1.95180i	−0.175244	+	0.0725883i
$724$	45.2049	−	13.6423i	1.68003	−	0.507011i
$725$	−3.32479	+	8.02675i	−0.123480	+	0.298106i
$726$	−7.64122	−	8.44289i	−0.283592	−	0.313345i
$727$	−6.99691	+	6.99691i	−0.259501	+	0.259501i	−0.824851	−	0.565350i	$-0.808741\pi$
$727$	−6.99691	+	6.99691i	−0.259501	+	0.259501i	0.565350	+	0.824851i	$0.308741\pi$
$728$	9.77177	+	1.47091i	0.362166	+	0.0545154i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	0.286243	−	5.74293i	0.0105943	−	0.212555i
$731$	−42.7683	−	17.7152i	−1.58184	−	0.655221i
$732$	24.4643	+	2.44480i	0.904226	+	0.0903625i
$733$	1.40532	+	3.39275i	0.0519068	+	0.125314i	0.947706	−	0.319145i	$-0.103396\pi$
$733$	1.40532	+	3.39275i	0.0519068	+	0.125314i	−0.895799	+	0.444459i	$0.853396\pi$
$734$	−14.9151	−	7.06736i	−0.550527	−	0.260861i
$735$	−10.9828			−0.405107
$736$	−3.57883	+	0.517818i	−0.131917	+	0.0190870i
$737$	−20.4037			−0.751578
$738$	−12.0194	−	5.69526i	−0.442441	−	0.209646i
$739$	−8.11566	−	19.5929i	−0.298539	−	0.720738i	−0.999968	−	0.00799797i	$-0.997454\pi$
$739$	−8.11566	−	19.5929i	−0.298539	−	0.720738i	0.701429	−	0.712740i	$-0.252546\pi$
$740$	0.303844	−	3.04046i	0.0111695	−	0.111769i
$741$	−16.6517	−	6.89737i	−0.611717	−	0.253381i
$742$	−0.169854	+	3.40781i	−0.00623555	+	0.125105i
$743$	5.67248	+	5.67248i	0.208103	+	0.208103i	0.803461	−	0.595358i	$-0.202990\pi$
$743$	5.67248	+	5.67248i	0.208103	+	0.208103i	−0.595358	+	0.803461i	$0.702990\pi$
$744$	−15.6714	−	21.2253i	−0.574540	−	0.778156i
$745$	6.90277	−	6.90277i	0.252898	−	0.252898i
$746$	−26.2308	−	28.9828i	−0.960378	−	1.06114i
$747$	−1.38172	+	3.33576i	−0.0505544	+	0.122049i
$748$	7.90227	+	26.1849i	0.288936	+	0.957413i
$749$	6.38513	−	2.64481i	0.233307	−	0.0966391i
$750$	5.76937	+	16.1607i	0.210668	+	0.590104i
$751$		−	14.2209i		−	0.518930i	−0.965753	−	0.259465i	$-0.916454\pi$
$751$		−	14.2209i		−	0.518930i	0.965753	−	0.259465i	$-0.0835462\pi$
$752$	33.3472	+	6.73225i	1.21605	+	0.245500i
$753$		−	16.9655i		−	0.618258i
$754$	−24.6708	+	8.80747i	−0.898456	+	0.320749i
$755$	23.3016	−	9.65183i	0.848031	−	0.351266i
$756$	−0.788013	+	1.46922i	−0.0286598	+	0.0534349i
$757$	−6.45206	+	15.5767i	−0.234504	+	0.566143i	−0.996697	−	0.0812065i	$-0.974123\pi$
$757$	−6.45206	+	15.5767i	−0.234504	+	0.566143i	0.762193	+	0.647350i	$0.224123\pi$
$758$	12.7970	−	11.5819i	0.464807	−	0.420672i
$759$	−0.776088	+	0.776088i	−0.0281702	+	0.0281702i
$760$	−20.5633	+	5.10405i	−0.745909	+	0.185143i
$761$	−8.62429	−	8.62429i	−0.312630	−	0.312630i	0.533298	−	0.845928i	$-0.320953\pi$
$761$	−8.62429	−	8.62429i	−0.312630	−	0.312630i	−0.845928	+	0.533298i	$0.820953\pi$
$762$	11.2112	+	0.558796i	0.406139	+	0.0202431i
$763$	−9.06398	−	3.75442i	−0.328138	−	0.135919i
$764$	−20.2298	−	24.7220i	−0.731889	−	0.894411i
$765$	−5.30942	−	12.8181i	−0.191963	−	0.463439i
$766$	−8.63828	+	18.2304i	−0.312114	+	0.658692i
$767$	−8.71912			−0.314829
$768$	−0.0913993	+	15.9997i	−0.00329809	+	0.577341i
$769$	13.1949			0.475821			0.237911	−	0.971287i	$-0.423537\pi$
$769$	13.1949			0.475821			0.237911	+	0.971287i	$0.423537\pi$
$770$	1.50974	−	3.18619i	0.0544073	−	0.114822i
$771$	−4.89528	−	11.8183i	−0.176299	−	0.425624i
$772$	−0.520726	−	0.636358i	−0.0187413	−	0.0229030i
$773$	−23.3275	−	9.66257i	−0.839032	−	0.347538i	−0.0785601	−	0.996909i	$-0.525032\pi$
$773$	−23.3275	−	9.66257i	−0.839032	−	0.347538i	−0.760472	+	0.649371i	$0.775032\pi$
$774$	−8.20912	−	0.409164i	−0.295071	−	0.0147071i
$775$	12.9664	+	12.9664i	0.465768	+	0.465768i
$776$	9.08435	−	2.25484i	0.326109	−	0.0809441i
$777$	−0.516999	+	0.516999i	−0.0185472	+	0.0185472i
$778$	19.2569	−	17.4284i	0.690394	−	0.624839i
$779$	−15.4775	+	37.3660i	−0.554539	+	1.33877i
$780$	−6.90130	+	12.8672i	−0.247106	+	0.460719i
$781$	−20.4130	+	8.45534i	−0.730434	+	0.302556i
$782$	−6.78139	+	2.42096i	−0.242502	+	0.0865733i
$783$		−	4.41958i		−	0.157943i
$784$	24.7217	+	4.99089i	0.882917	+	0.178246i
$785$			21.1247i			0.753971i
$786$	8.95538	+	25.0851i	0.319428	+	0.894754i
$787$	12.3210	−	5.10352i	0.439196	−	0.181921i	−0.152118	−	0.988362i	$-0.548609\pi$
$787$	12.3210	−	5.10352i	0.439196	−	0.181921i	0.591314	+	0.806442i	$0.298609\pi$
$788$	2.56262	+	8.49146i	0.0912895	+	0.302496i
$789$	−2.74252	+	6.62104i	−0.0976364	+	0.235715i
$790$	−0.959527	−	1.06019i	−0.0341384	−	0.0377200i
$791$	−0.623152	+	0.623152i	−0.0221567	+	0.0221567i
$792$	2.88453	+	3.90681i	0.102497	+	0.138822i
$793$	−36.4318	−	36.4318i	−1.29373	−	1.29373i
$794$	0.970901	−	19.4793i	0.0344560	−	0.691295i
$795$	−4.65776	−	1.92931i	−0.165194	−	0.0684255i
$796$	−2.43483	+	24.3645i	−0.0863003	+	0.863576i
$797$	−0.0303911	−	0.0733705i	−0.00107651	−	0.00259892i	0.923340	−	0.383983i	$-0.125448\pi$
$797$	−0.0303911	−	0.0733705i	−0.00107651	−	0.00259892i	−0.924417	+	0.381384i	$0.875448\pi$
$798$	4.58141	+	2.17085i	0.162180	+	0.0768473i
$799$	67.7425			2.39656
$800$	−1.59241	−	11.0057i	−0.0563002	−	0.389112i
$801$	6.95069			0.245590
$802$	26.3940	+	12.5065i	0.932004	+	0.441620i
$803$	1.53369	+	3.70265i	0.0541226	+	0.130664i
$804$	−23.6494	−	2.36336i	−0.834048	−	0.0833494i
$805$	0.857551	+	0.355209i	0.0302247	+	0.0125195i
$806$	−2.75236	+	55.2209i	−0.0969476	+	1.94507i
$807$	12.5924	+	12.5924i	0.443272	+	0.443272i
$808$	7.84494	+	1.18087i	0.275984	+	0.0415428i
$809$	−6.49942	+	6.49942i	−0.228507	+	0.228507i	−0.812069	−	0.583562i	$-0.801659\pi$
$809$	−6.49942	+	6.49942i	−0.228507	+	0.228507i	0.583562	+	0.812069i	$0.301659\pi$
$810$	−1.65302	−	1.82644i	−0.0580811	−	0.0641747i
$811$	6.45066	−	15.5733i	0.226513	−	0.546852i	−0.769235	−	0.638966i	$-0.779362\pi$
$811$	6.45066	−	15.5733i	0.226513	−	0.546852i	0.995748	+	0.0921142i	$0.0293625\pi$
$812$	7.05411	−	2.12884i	0.247551	−	0.0747078i
$813$	5.91417	−	2.44973i	0.207419	−	0.0859157i
$814$	0.716048	+	2.00573i	0.0250975	+	0.0703009i
$815$			4.46935i			0.156555i
$816$	6.12632	+	31.2655i	0.214464	+	1.09451i
$817$			24.9936i			0.874417i
$818$	12.0185	−	4.29062i	0.420218	−	0.150018i
$819$	3.22782	−	1.33701i	0.112789	−	0.0467187i
$820$	28.8736	+	15.4863i	1.00831	+	0.540805i
$821$	−20.6508	+	49.8554i	−0.720717	+	1.73996i	−0.0494163	+	0.998778i	$0.515736\pi$
$821$	−20.6508	+	49.8554i	−0.720717	+	1.73996i	−0.671300	+	0.741185i	$0.734264\pi$
$822$	−0.453360	+	0.410312i	−0.0158127	+	0.0143113i
$823$	−22.2511	+	22.2511i	−0.775623	+	0.775623i	−0.979083	−	0.203460i	$-0.934781\pi$
$823$	−22.2511	+	22.2511i	−0.775623	+	0.775623i	0.203460	+	0.979083i	$0.434781\pi$
$824$	−43.7140	−	26.3286i	−1.52285	−	0.917201i
$825$	−2.38665	−	2.38665i	−0.0830925	−	0.0830925i
$826$	2.44947	+	0.122088i	0.0852280	+	0.00424799i
$827$	−34.4764	−	14.2806i	−1.19886	−	0.496584i	−0.308230	−	0.951312i	$-0.599737\pi$
$827$	−34.4764	−	14.2806i	−1.19886	−	0.496584i	−0.890631	+	0.454728i	$0.849737\pi$
$828$	−0.989438	+	0.809649i	−0.0343854	+	0.0281373i
$829$	−0.158799	−	0.383374i	−0.00551531	−	0.0133151i	0.921098	−	0.389331i	$-0.127294\pi$
$829$	−0.158799	−	0.383374i	−0.00551531	−	0.0133151i	−0.926613	+	0.376016i	$0.877294\pi$
$830$	3.80857	−	8.03770i	0.132198	−	0.278993i
$831$	−5.24655			−0.182001
$832$	21.3816	−	25.8272i	0.741275	−	0.895395i
$833$	50.2203			1.74003
$834$	−10.6370	+	22.4487i	−0.368331	+	0.777333i
$835$	−6.43949	−	15.5463i	−0.222848	−	0.538002i
$836$	11.4286	−	9.35194i	0.395267	−	0.323444i
$837$	−8.61802	−	3.56970i	−0.297882	−	0.123387i
$838$	−31.2329	−	1.55673i	−1.07892	−	0.0537763i
$839$	19.2723	+	19.2723i	0.665353	+	0.665353i	0.956637	−	0.291284i	$-0.0940825\pi$
$839$	19.2723	+	19.2723i	0.665353	+	0.665353i	−0.291284	+	0.956637i	$0.594082\pi$
$840$	2.11896	−	3.51816i	0.0731111	−	0.121388i
$841$	6.69439	−	6.69439i	0.230841	−	0.230841i
$842$	−32.0893	+	29.0424i	−1.10587	+	1.00087i
$843$	4.88559	−	11.7949i	0.168269	−	0.406237i
$844$	8.61340	+	4.61979i	0.296486	+	0.159020i
$845$	7.34785	−	3.04358i	0.252774	−	0.104702i
$846$	11.3277	−	4.04398i	0.389453	−	0.139035i
$847$		−	6.71219i		−	0.230634i
$848$	9.60762	+	6.45938i	0.329927	+	0.221816i
$849$		−	8.56633i		−	0.293996i
$850$	−7.44501	−	20.8543i	−0.255362	−	0.715298i
$851$	−0.517996	+	0.214561i	−0.0177567	+	0.00735505i
$852$	−24.6396	+	7.43592i	−0.844137	+	0.254750i
$853$	11.9556	−	28.8634i	0.409352	−	0.988263i	−0.575957	−	0.817480i	$-0.695370\pi$
$853$	11.9556	−	28.8634i	0.409352	−	0.988263i	0.985309	−	0.170783i	$-0.0546297\pi$
$854$	9.72469	+	10.7449i	0.332772	+	0.367685i
$855$	−5.29682	+	5.29682i	−0.181147	+	0.181147i
$856$	3.49049	−	23.1886i	0.119303	−	0.792572i
$857$	−7.59541	−	7.59541i	−0.259454	−	0.259454i	0.565378	−	0.824832i	$-0.308730\pi$
$857$	−7.59541	−	7.59541i	−0.259454	−	0.259454i	−0.824832	+	0.565378i	$0.808730\pi$
$858$	0.506609	−	10.1642i	0.0172954	−	0.346999i
$859$	31.8605	+	13.1970i	1.08707	+	0.450277i	0.852983	−	0.521939i	$-0.174791\pi$
$859$	31.8605	+	13.1970i	1.08707	+	0.450277i	0.234083	+	0.972217i	$0.424791\pi$
$860$	20.1471	+	2.01337i	0.687011	+	0.0686555i
$861$	−3.00020	−	7.24312i	−0.102246	−	0.246845i
$862$	10.6079	+	5.02643i	0.361306	+	0.171201i
$863$	−10.7216			−0.364968			−0.182484	−	0.983209i	$-0.558414\pi$
$863$	−10.7216			−0.364968			−0.182484	+	0.983209i	$0.558414\pi$
$864$	2.89086	+	4.86240i	0.0983491	+	0.165422i
$865$	5.21630			0.177360
$866$	−37.6066	−	17.8194i	−1.27792	−	0.605530i
$867$	17.7724	+	42.9064i	0.603583	+	1.45718i
$868$	1.54644	−	15.4747i	0.0524898	−	0.525246i
$869$	0.920779	+	0.381399i	0.0312353	+	0.0129381i
$870$	−0.541975	+	10.8737i	−0.0183747	+	0.368654i
$871$	35.2182	+	35.2182i	1.19332	+	1.19332i
$872$	−26.7797	+	19.7724i	−0.906876	+	0.669579i
$873$	2.34000	−	2.34000i	0.0791971	−	0.0791971i
$874$	2.60874	+	2.88244i	0.0882420	+	0.0974999i
$875$	−3.87071	+	9.34473i	−0.130854	+	0.315910i
$876$	1.34878	+	4.46929i	0.0455710	+	0.151003i
$877$	8.29027	−	3.43394i	0.279943	−	0.115956i	−0.238295	−	0.971193i	$-0.576588\pi$
$877$	8.29027	−	3.43394i	0.279943	−	0.115956i	0.518237	+	0.855237i	$0.326588\pi$
$878$	−13.6597	−	38.2624i	−0.460992	−	1.29129i
$879$			1.19722i			0.0403812i
$880$	−6.61787	−	9.96585i	−0.223088	−	0.335949i
$881$		−	13.4623i		−	0.453557i	−0.973946	−	0.226779i	$-0.927181\pi$
$881$		−	13.4623i		−	0.453557i	0.973946	−	0.226779i	$-0.0728194\pi$
$882$	8.39767	−	2.99797i	0.282764	−	0.100947i
$883$	28.1854	−	11.6748i	0.948513	−	0.392887i	0.145841	−	0.989308i	$-0.453411\pi$
$883$	28.1854	−	11.6748i	0.948513	−	0.392887i	0.802672	+	0.596421i	$0.203411\pi$
$884$	31.5571	−	58.8369i	1.06138	−	1.97890i
$885$	−1.38675	+	3.34791i	−0.0466151	+	0.112539i
$886$	20.5615	−	18.6091i	0.690777	−	0.625186i
$887$	12.7798	−	12.7798i	0.429102	−	0.429102i	−0.459220	−	0.888322i	$-0.651871\pi$
$887$	12.7798	−	12.7798i	0.429102	−	0.429102i	0.888322	+	0.459220i	$0.151871\pi$
$888$	0.597628	+	2.40773i	0.0200551	+	0.0807983i
$889$	4.67864	+	4.67864i	0.156917	+	0.156917i
$890$	−17.1011	−	0.852366i	−0.573231	−	0.0285714i
$891$	1.58627	+	0.657053i	0.0531419	+	0.0220121i
$892$	10.2236	+	12.4938i	0.342311	+	0.418324i
$893$	−13.9966	−	33.7908i	−0.468379	−	1.13077i
$894$	−3.39375	+	7.16224i	−0.113504	+	0.239541i
$895$	−25.2369			−0.843578
$896$	−6.36841	+	6.95626i	−0.212754	+	0.232392i
$897$	2.67917			0.0894548
$898$	−4.97081	+	10.4905i	−0.165878	+	0.350073i
$899$	15.7766	+	38.0880i	0.526179	+	1.27031i
$900$	−2.48986	−	3.04275i	−0.0829953	−	0.101425i
$901$	21.2982	+	8.82201i	0.709547	+	0.293904i
$902$	−22.8081	−	1.13682i	−0.759426	−	0.0378518i
$903$	−3.42581	−	3.42581i	−0.114004	−	0.114004i
$904$	0.720336	+	2.90211i	0.0239580	+	0.0965226i
$905$	−29.0796	+	29.0796i	−0.966639	+	0.966639i
$906$	−15.1822	+	13.7406i	−0.504394	+	0.456501i
$907$	−20.4543	+	49.3811i	−0.679175	+	1.63967i	0.0863491	+	0.996265i	$0.472480\pi$
$907$	−20.4543	+	49.3811i	−0.679175	+	1.63967i	−0.765524	+	0.643408i	$0.777520\pi$
$908$	−2.45376	+	4.57493i	−0.0814308	+	0.151824i
$909$	2.59134	−	1.07337i	0.0859494	−	0.0356014i
$910$	−8.10552	+	2.89367i	−0.268695	+	0.0959243i
$911$			19.5928i			0.649138i	0.945862	+	0.324569i	$0.105219\pi$
$911$			19.5928i			0.649138i	−0.945862	+	0.324569i	$0.894781\pi$
$912$	14.3299	−	9.51581i	0.474509	−	0.315100i
$913$			6.19927i			0.205166i
$914$	8.20746	+	22.9900i	0.271479	+	0.760443i
$915$	−19.7832	+	8.19447i	−0.654012	+	0.270901i
$916$	−5.91798	−	19.6097i	−0.195535	−	0.647924i
$917$	−6.00823	+	14.5052i	−0.198409	+	0.479003i
$918$	7.55864	+	8.35165i	0.249472	+	0.275646i
$919$	33.9389	−	33.9389i	1.11954	−	1.11954i	0.127732	−	0.991809i	$-0.459230\pi$
$919$	33.9389	−	33.9389i	1.11954	−	1.11954i	0.991809	−	0.127732i	$-0.0407696\pi$
$920$	2.53365	−	1.87069i	0.0835321	−	0.0616747i
$921$	−7.67932	−	7.67932i	−0.253042	−	0.253042i
$922$	−2.17941	+	43.7258i	−0.0717751	+	1.44003i
$923$	49.8288	+	20.6398i	1.64014	+	0.679366i
$924$	−0.284645	+	2.84834i	−0.00936412	+	0.0937035i
$925$	−0.659825	−	1.59296i	−0.0216949	−	0.0523761i
$926$	29.3114	+	13.8889i	0.963233	+	0.456417i
$927$	−18.0420			−0.592577
$928$	6.16128	−	24.2298i	0.202254	−	0.795383i
$929$	−42.5730			−1.39678			−0.698388	−	0.715720i	$-0.746099\pi$
$929$	−42.5730			−1.39678			−0.698388	+	0.715720i	$0.746099\pi$
$930$	20.7656	+	9.83955i	0.680931	+	0.322652i
$931$	−10.3763	−	25.0505i	−0.340069	−	0.820998i
$932$	−16.7414	−	1.67303i	−0.548384	−	0.0548020i
$933$	14.6220	+	6.05664i	0.478704	+	0.198286i
$934$	1.57382	−	31.5758i	0.0514970	−	1.03319i
$935$	−16.8443	−	16.8443i	−0.550868	−	0.550868i
$936$	1.76452	−	11.7223i	0.0576751	−	0.383157i
$937$	−13.0124	+	13.0124i	−0.425098	+	0.425098i	−0.886954	−	0.461857i	$-0.847183\pi$
$937$	−13.0124	+	13.0124i	−0.425098	+	0.425098i	0.461857	+	0.886954i	$0.347183\pi$
$938$	−9.40075	−	10.3870i	−0.306945	−	0.339148i
$939$	8.19864	−	19.7933i	0.267553	−	0.645929i
$940$	−28.3660	+	8.56050i	−0.925196	+	0.279213i
$941$	12.9144	−	5.34932i	0.420998	−	0.174383i	−0.162119	−	0.986771i	$-0.551833\pi$
$941$	12.9144	−	5.34932i	0.420998	−	0.174383i	0.583117	+	0.812388i	$0.301833\pi$
$942$	−5.76639	−	16.1523i	−0.187879	−	0.526271i
$943$		−	6.01197i		−	0.195777i
$944$	4.64288	−	6.90578i	0.151113	−	0.224764i
$945$		−	1.45204i		−	0.0472350i
$946$	−13.2907	+	4.74478i	−0.432118	+	0.154266i
$947$	1.72532	−	0.714653i	0.0560655	−	0.0232231i	−0.354474	−	0.935066i	$-0.615340\pi$
$947$	1.72532	−	0.714653i	0.0560655	−	0.0232231i	0.410540	+	0.911843i	$0.365340\pi$
$948$	1.02307	+	0.548724i	0.0332279	+	0.0178217i
$949$	3.74378	−	9.03829i	0.121528	−	0.293395i
$950$	−8.86416	+	8.02249i	−0.287591	+	0.260284i
$951$	−4.63622	+	4.63622i	−0.150340	+	0.150340i
$952$	−9.68922	+	16.0872i	−0.314029	+	0.521390i
$953$	19.2732	+	19.2732i	0.624321	+	0.624321i	0.946633	−	0.322312i	$-0.104460\pi$
$953$	19.2732	+	19.2732i	0.624321	+	0.624321i	−0.322312	+	0.946633i	$0.604460\pi$
$954$	4.08806	+	0.203760i	0.132356	+	0.00659697i
$955$	25.7038	+	10.6468i	0.831754	+	0.344524i
$956$	3.20646	−	2.62382i	0.103704	−	0.0848605i
$957$	−2.90390	−	7.01063i	−0.0938698	−	0.226622i
$958$	−25.3317	+	53.4605i	−0.818429	+	1.72723i
$959$	−0.360426			−0.0116388
$960$	−6.51626	−	12.3177i	−0.210311	−	0.397552i
$961$	56.0131			1.80687
$962$	2.22609	−	4.69799i	0.0717720	−	0.151469i
$963$	−3.17275	−	7.65969i	−0.102240	−	0.246830i
$964$	−7.89441	+	6.45993i	−0.254262	+	0.208060i
$965$	0.661628	+	0.274055i	0.0212986	+	0.00882215i
$966$	−0.752662	−	0.0375147i	−0.0242165	−	0.00120701i
$967$	−39.5173	−	39.5173i	−1.27079	−	1.27079i	−0.945674	−	0.325118i	$-0.894596\pi$
$967$	−39.5173	−	39.5173i	−1.27079	−	1.27079i	−0.325118	−	0.945674i	$-0.605404\pi$
$968$	−19.5093	−	11.7503i	−0.627053	−	0.377669i
$969$	24.2204	−	24.2204i	0.778071	−	0.778071i
$970$	−6.04418	+	5.47027i	−0.194067	+	0.175640i
$971$	−1.47350	+	3.55734i	−0.0472868	+	0.114161i	−0.945758	−	0.324872i	$-0.894679\pi$
$971$	−1.47350	+	3.55734i	−0.0472868	+	0.114161i	0.898471	+	0.439033i	$0.144679\pi$
$972$	1.76249	+	0.945311i	0.0565320	+	0.0303209i
$973$	−13.5280	+	5.60347i	−0.433687	+	0.179639i
$974$	7.58694	−	2.70854i	0.243101	−	0.0867872i
$975$			8.23907i			0.263861i
$976$	48.2546	−	9.45525i	1.54459	−	0.302655i
$977$			11.1620i			0.357103i	0.983931	+	0.178551i	$0.0571410\pi$
$977$			11.1620i			0.357103i	−0.983931	+	0.178551i	$0.942859\pi$
$978$	−1.22000	−	3.41735i	−0.0390112	−	0.109275i
$979$	11.0256	−	4.56697i	0.352381	−	0.145961i
$980$	−21.0289	+	6.34626i	−0.671743	+	0.202724i
$981$	−4.50386	+	10.8733i	−0.143797	+	0.347157i
$982$	−39.0851	−	43.1857i	−1.24726	−	1.37811i
$983$	−14.2055	+	14.2055i	−0.453085	+	0.453085i	−0.896377	−	0.443292i	$-0.853810\pi$
$983$	−14.2055	+	14.2055i	−0.453085	+	0.453085i	0.443292	+	0.896377i	$0.353810\pi$
$984$	−26.3046	−	3.95952i	−0.838559	−	0.126225i
$985$	−5.46242	−	5.46242i	−0.174047	−	0.174047i
$986$	2.47825	−	49.7215i	0.0789236	−	1.58346i
$987$	6.55010	+	2.71314i	0.208492	+	0.0863602i
$988$	−35.8688	−	3.58449i	−1.14114	−	0.114038i
$989$	−1.42176	−	3.43242i	−0.0452092	−	0.109145i
$990$	−3.82220	−	1.81111i	−0.121477	−	0.0575607i
$991$	−31.5264			−1.00147			−0.500734	−	0.865601i	$-0.666937\pi$
$991$	−31.5264			−1.00147			−0.500734	+	0.865601i	$0.666937\pi$
$992$	−42.2708	−	31.5847i	−1.34210	−	1.00282i
$993$	−19.6735			−0.624321
$994$	−13.7095	−	6.49608i	−0.434838	−	0.206043i
$995$	−8.16104	−	19.7025i	−0.258722	−	0.624611i
$996$	−0.718064	+	7.18541i	−0.0227527	+	0.227678i
$997$	−25.5314	−	10.5755i	−0.808588	−	0.334928i	−0.0601976	−	0.998186i	$-0.519173\pi$
$997$	−25.5314	−	10.5755i	−0.808588	−	0.334928i	−0.748391	+	0.663258i	$0.769173\pi$
$998$	0.574006	−	11.5164i	0.0181698	−	0.364544i
$999$	0.620199	+	0.620199i	0.0196222	+	0.0196222i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	96.2.n.a.37.5	yes	32
3.2	odd	2		288.2.v.d.37.4		32
4.3	odd	2		384.2.n.a.241.7		32
8.3	odd	2		768.2.n.b.481.2		32
8.5	even	2		768.2.n.a.481.6		32
12.11	even	2		1152.2.v.c.1009.3		32
32.3	odd	8		768.2.n.b.289.2		32
32.13	even	8	inner	96.2.n.a.13.5	✓	32
32.19	odd	8		384.2.n.a.145.7		32
32.29	even	8		768.2.n.a.289.6		32
96.77	odd	8		288.2.v.d.109.4		32
96.83	even	8		1152.2.v.c.145.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.13.5	✓	32	32.13	even	8	inner
96.2.n.a.37.5	yes	32	1.1	even	1	trivial
288.2.v.d.37.4		32	3.2	odd	2
288.2.v.d.109.4		32	96.77	odd	8
384.2.n.a.145.7		32	32.19	odd	8
384.2.n.a.241.7		32	4.3	odd	2
768.2.n.a.289.6		32	32.29	even	8
768.2.n.a.481.6		32	8.5	even	2
768.2.n.b.289.2		32	32.3	odd	8
768.2.n.b.481.2		32	8.3	odd	2
1152.2.v.c.145.3		32	96.83	even	8
1152.2.v.c.1009.3		32	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	96.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.605567 - 1.27800i) q^{2} +(-0.382683 - 0.923880i) q^{3} +(-1.26658 - 1.54783i) q^{4} +(1.60930 + 0.666593i) q^{5} +(-1.41246 - 0.0704008i) q^{6} +(-0.589445 - 0.589445i) q^{7} +(-2.74513 + 0.681373i) q^{8} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(0.605567 - 1.27800i) q^{2} +(-0.382683 - 0.923880i) q^{3} +(-1.26658 - 1.54783i) q^{4} +(1.60930 + 0.666593i) q^{5} +(-1.41246 - 0.0704008i) q^{6} +(-0.589445 - 0.589445i) q^{7} +(-2.74513 + 0.681373i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(1.82644 - 1.65302i) q^{10} +(-0.657053 + 1.58627i) q^{11} +(-0.945311 + 1.76249i) q^{12} +(3.87213 - 1.60389i) q^{13} +(-1.11026 + 0.396364i) q^{14} -1.74189i q^{15} +(-0.791564 + 3.92090i) q^{16} +7.96502i q^{17} +(0.475483 + 1.33188i) q^{18} +(3.97306 - 1.64569i) q^{19} +(-1.00653 - 3.33521i) q^{20} +(-0.319006 + 0.770147i) q^{21} +(1.62936 + 1.80031i) q^{22} +(-0.452012 + 0.452012i) q^{23} +(1.68002 + 2.27542i) q^{24} +(-1.39004 - 1.39004i) q^{25} +(0.295061 - 5.91986i) q^{26} +(0.923880 + 0.382683i) q^{27} +(-0.165784 + 1.65894i) q^{28} +(-1.69130 - 4.08316i) q^{29} +(-2.22614 - 1.05483i) q^{30} -9.32808 q^{31} +(4.53157 + 3.38598i) q^{32} +1.71696 q^{33} +(10.1793 + 4.82335i) q^{34} +(-0.555673 - 1.34151i) q^{35} +(1.99009 + 0.198877i) q^{36} +(0.810329 + 0.335649i) q^{37} +(0.302752 - 6.07415i) q^{38} +(-2.96360 - 2.96360i) q^{39} +(-4.87193 - 0.733351i) q^{40} +(-6.65023 + 6.65023i) q^{41} +(0.791071 + 0.874066i) q^{42} +(-2.22413 + 5.36952i) q^{43} +(3.28748 - 0.992122i) q^{44} +(-1.60930 + 0.666593i) q^{45} +(0.303949 + 0.851396i) q^{46} -8.50500i q^{47} +(3.92535 - 0.769153i) q^{48} -6.30511i q^{49} +(-2.61824 + 0.934713i) q^{50} +(7.35872 - 3.04808i) q^{51} +(-7.38691 - 3.96196i) q^{52} +(1.10759 - 2.67397i) q^{53} +(1.04854 - 0.948979i) q^{54} +(-2.11479 + 2.11479i) q^{55} +(2.01974 + 1.21647i) q^{56} +(-3.04084 - 3.04084i) q^{57} +(-6.24248 - 0.311142i) q^{58} +(-1.92200 - 0.796118i) q^{59} +(-2.69615 + 2.20624i) q^{60} +(-4.70435 - 11.3573i) q^{61} +(-5.64878 + 11.9213i) q^{62} +0.833602 q^{63} +(7.07146 - 3.74091i) q^{64} +7.30055 q^{65} +(1.03974 - 2.19428i) q^{66} +(4.54765 + 10.9790i) q^{67} +(12.3285 - 10.0883i) q^{68} +(0.590582 + 0.244627i) q^{69} +(-2.05095 - 0.102225i) q^{70} +(9.09946 + 9.09946i) q^{71} +(1.45930 - 2.42290i) q^{72} +(1.65052 - 1.65052i) q^{73} +(0.919668 - 0.832343i) q^{74} +(-0.752286 + 1.81618i) q^{75} +(-7.57944 - 4.06522i) q^{76} +(1.32231 - 0.547721i) q^{77} +(-5.58215 + 1.99283i) q^{78} -0.580469i q^{79} +(-3.88750 + 5.78224i) q^{80} -1.00000i q^{81} +(4.47185 + 12.5262i) q^{82} +(3.33576 - 1.38172i) q^{83} +(1.59610 - 0.481685i) q^{84} +(-5.30942 + 12.8181i) q^{85} +(5.51540 + 6.09404i) q^{86} +(-3.12512 + 3.12512i) q^{87} +(0.722857 - 4.80220i) q^{88} +(-4.91488 - 4.91488i) q^{89} +(-0.122630 + 2.46035i) q^{90} +(-3.22782 - 1.33701i) q^{91} +(1.27215 + 0.127130i) q^{92} +(3.56970 + 8.61802i) q^{93} +(-10.8694 - 5.15035i) q^{94} +7.49083 q^{95} +(1.39409 - 5.48238i) q^{96} -3.30926 q^{97} +(-8.05794 - 3.81817i) q^{98} +(-0.657053 - 1.58627i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} - 16 q^{12} - 32 q^{14} - 8 q^{16} - 8 q^{18} - 32 q^{20} - 8 q^{22} - 16 q^{23} - 8 q^{24} + 40 q^{26} + 40 q^{28} - 48 q^{31} + 40 q^{32} + 40 q^{34} - 48 q^{35} + 40 q^{38} + 8 q^{40} - 16 q^{43} + 8 q^{44} - 32 q^{46} + 24 q^{50} + 16 q^{51} - 8 q^{52} - 32 q^{53} + 8 q^{54} + 32 q^{55} + 56 q^{56} - 32 q^{58} + 64 q^{59} + 48 q^{60} - 32 q^{61} + 48 q^{62} + 16 q^{63} + 24 q^{64} + 48 q^{66} + 16 q^{67} - 8 q^{68} - 32 q^{69} - 24 q^{70} + 64 q^{71} - 32 q^{74} + 32 q^{75} - 56 q^{76} - 32 q^{77} + 24 q^{78} - 56 q^{80} - 40 q^{82} - 64 q^{86} - 48 q^{88} - 48 q^{91} - 80 q^{92} - 32 q^{94} - 40 q^{96} - 80 q^{98}+O(q^{100}) \) 32 * q - 8 * q^10 - 16 * q^12 - 32 * q^14 - 8 * q^16 - 8 * q^18 - 32 * q^20 - 8 * q^22 - 16 * q^23 - 8 * q^24 + 40 * q^26 + 40 * q^28 - 48 * q^31 + 40 * q^32 + 40 * q^34 - 48 * q^35 + 40 * q^38 + 8 * q^40 - 16 * q^43 + 8 * q^44 - 32 * q^46 + 24 * q^50 + 16 * q^51 - 8 * q^52 - 32 * q^53 + 8 * q^54 + 32 * q^55 + 56 * q^56 - 32 * q^58 + 64 * q^59 + 48 * q^60 - 32 * q^61 + 48 * q^62 + 16 * q^63 + 24 * q^64 + 48 * q^66 + 16 * q^67 - 8 * q^68 - 32 * q^69 - 24 * q^70 + 64 * q^71 - 32 * q^74 + 32 * q^75 - 56 * q^76 - 32 * q^77 + 24 * q^78 - 56 * q^80 - 40 * q^82 - 64 * q^86 - 48 * q^88 - 48 * q^91 - 80 * q^92 - 32 * q^94 - 40 * q^96 - 80 * q^98

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